Maximum Likelihood Estimation Method Research Articles

Tomographic cross correlations between galaxy surveys and the CMB gravitational lensing potential. Effect of the redshift bin mismatch

Upcoming surveys of the large-scale structure of our Universe will employ a large coverage area of about half of the sky and will significantly increase the observational depth. With these surveys, we will be able to cross-correlate cosmic microwave background (CMB) gravitational lensing and galaxy surveys divided into narrow redshift bins to map the evolution of the cosmological parameters with redshift. We study the effect of the redshift bin mismatch of objects that is due to photometric redshift errors in tomographic cross-correlation measurements. We used the code FLASK to create Monte Carlo simulations of the Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST) and Planck CMB lensing convergence. We simulated log-normal fields and divided galaxies into nine redshift bins with the Gaussian and modified Lorentzian photometric redshift errors. To estimate the parameters, we used angular power spectra of CMB lensing and galaxy density contrast fields and the maximum likelihood estimation method. We show that even with simple Gaussian errors with a standard deviation of $ the galaxy auto-power spectra in tomographic bins are offset by $2-15<!PCT!>$. The estimated cross-power spectra between galaxy clustering and CMB lensing are also biased, with smaller deviations $<5<!PCT!>$. As a result, the $ $ parameter deviates between $0.2-1.2\ due to the redshift bin mismatch of the objects. We propose a computationally fast and robust method based on the scattering matrix approach to correct for the redshift bin mismatch of the objects. The estimates of the parameters in tomographic studies such as the linear galaxy bias, the cross-correlation amplitude, and $ $ are biased due to the redshift bin mismatch of the objects. The biases in these parameters are alleviated with our scattering matrix approach.

A STOCHASTIC MODEL FOR LENGTH BIASED LOAI DISTRIBUTION WITH PROPERTIES AND ITS APPLICATIONS

One of the most important applications of statistical analysis is in health research and application. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. In this paper, we examine some general models leading to a weighted distribution. The developed distribution, also known as the length biased model, is referred to as the length biased Loai distribution. This distribution is a specific type of basic distribution, the Loai distribution. The length biased distribution has been compared with the original distribution. Some statistical properties of this distribution are derived, such as moments, the moment generating function, the reliability analysis, and the included functions. Also, the distribution of order statistics, quantile function, and likelihood ratio test are presented. The Bonferroni and Lorenz carvers, as well as the Rnyi and Tsallis entropies, are derived. The method of maximum likelihood estimation is used to estimate the distribution parameters. A simulation study is performed to investigate the performance of the estimation. The real data applications demonstrate that the proposed distribution can provide better results than several well-known distributions.

Reliability evaluation for Weibull distribution with heavily Type II censored data

AbstractThe lifetime data collected from the field are usually heavily censored, in which case, getting an accurate reliability evaluation based on heavily censored data is challenging. For heavily Type‐II censored data, the parameters estimation bias of traditional methods (i.e., maximum likelihood estimation (MLE) and least squares estimation (LSE)) are still large, and Bayesian methods are hard to specify the priors in practice. Therefore, considering the existing range of shape parameter for Weibull distribution, this study proposes two novel parameter estimation methods, the three‐step MLE method and the hybrid estimation method. For the three‐step MLE method, the initial estimates of shape and scale parameters are first respectively derived using MLE, then are updated by the single parameter MLE method with the range constraint of shape parameter. For the hybrid estimation method, the shape parameter is estimated by the LSE method with the existing range constraint of shape parameter, then the scale parameter estimate can be obtained by MLE. On this basis, two numerical examples are performed to demonstrate the consistency and effectiveness of the proposed methods. Finally, a case study on turbine engines is given to verify the effectiveness and applicability of the proposed methods.

Development of mobile CAT for patient feedback on pediatric consultations based on Rasch analysis of online techniques.

The Rasch Rating Scale Model (RSM) is widely used in questionnaire analysis, providing insights into how individuals respond to item-level stimuli. Existing software for Rasch RSM parameter estimation, while powerful, often presents a steep learning curve. An accessible online tool can greatly benefit novice users, particularly students and clinicians, by simplifying the analytical process. This study introduces an online tool, an intuitive online RSM analysis tool designed to facilitate questionnaire data analysis for applied researchers, students, and clinicians. The online tool employs the joint maximum likelihood method for estimation, yielding estimates, standard errors (SE), and fit statistics iteratively. A unique feature of the tool is its ability to visualize estimates on Google Maps with an opacity setting of 0, enhancing data interpretation through a user-friendly interface. This study outlines the estimation process and key features, employing data from 200 proxy participants who answered 20 5-point questions regarding doctor-patient and doctor-family interactions in pediatric consultations. Mobile computerized adaptive testing (CAT) was employed. The online tool offers 5 essential visual displays often utilized in Rasch analyses, including the Wright Map, KIDMAP, category probability curve, performance plot, and differential item functioning (DIF) graph. DIF analysis revealed that 2 items, concerning the doctor attentiveness and empathy toward the child illness, exhibited differences in female proxy participants' responses, indicating lower satisfaction with pediatricians. The online tool emerges as a user-friendly and efficient RSM analysis tool with notable advantages for newcomers, improving data visualization and comprehension. Its capacity to pinpoint key areas of concern, such as gender-related satisfaction disparities among proxy participants, enhances its utility in questionnaire analysis. The online tool holds promise as a valuable resource for researchers, students, and clinicians seeking accessible Rasch analysis solutions.

APPLICATION OF GENERALIZED EXTREME VALUE DISTRIBUTION TO ANNUAL MAXIMUM RAINFALL

Generalized Extreme Value Distributions was used to model annual maximum rainfall data in Akure, Ondo State, Nigeria from 1981-2019. The parameters of the distribution are estimated using the maximum likelihood estimation method. The model fit indicated that the shape  parameter is negative this suggests that Fréchet distribution is the appropriate model for describing annual maximum rainfall in Ondo-state Nigeria. The estimated return levels for different return periods revealed an increase in the value over the years.

Impact of LS Mutation on Pharmacokinetics of Preventive HIV Broadly Neutralizing Monoclonal Antibodies: A Cross-Protocol Analysis of 16 Clinical Trials in People without HIV

Monoclonal antibodies are commonly engineered with an introduction of Met428Leu and Asn434Ser, known as the LS mutation, in the fragment crystallizable region to improve pharmacokinetic profiles. The LS mutation delays antibody clearance by enhancing binding affinity to the neonatal fragment crystallizable receptor found on endothelial cells. To characterize the LS mutation for monoclonal antibodies targeting HIV, we compared pharmacokinetic parameters between parental versus LS variants for five pairs of anti-HIV immunoglobin G1 monoclonal antibodies (VRC01/LS/VRC07-523LS, 3BNC117/LS, PGDM1400/LS PGT121/LS, 10-1074/LS), analyzing data from 16 clinical trials of 583 participants without HIV. We described serum concentrations of these monoclonal antibodies following intravenous or subcutaneous administration by an open two-compartment disposition, with first-order elimination from the central compartment using non-linear mixed effects pharmacokinetic models. We compared estimated pharmacokinetic parameters using the targeted maximum likelihood estimation method, accounting for participant differences. We observed lower clearance rate, central volume, and peripheral volume of distribution for all LS variants compared to parental monoclonal antibodies. LS monoclonal antibodies showed several improvements in pharmacokinetic parameters, including increases in the elimination half-life by 2.7- to 4.1-fold, the dose-normalized area-under-the-curve by 4.1- to 9.5-fold, and the predicted concentration at 4 weeks post-administration by 3.4- to 7.6-fold. Results suggest a favorable pharmacokinetic profile of LS variants regardless of HIV epitope specificity. Insights support lower dosages and/or less frequent dosing of LS variants to achieve similar levels of antibody exposure in future clinical applications.

Modelling Wind Speed, Humidity, and Temperature in Butterworth and Melaka during Southwest Monsoon in 2020 with a Simultaneous Linear Functional Relationship

The extension of parameter estimation from a bivariate linear functional relationship model (LFRM) to simultaneous LFRM for linear variables using the maximum likelihood estimation (MLE) method is explored in this paper. The covariance matrix of the parameter estimates is derived through the Fisher information matrix. A simulation study was done to investigate the performance of the parameter estimation. According to the simulation study, the estimated parameters have a small bias. The beauty of simultaneous LFRM lies in developing the model to study the relationship between more than two linear variables while considering error terms for all variables. The applicability of the proposed simultaneous model is demonstrated using wind speed, humidity, and temperature data from Butterworth and Melaka during the southwest monsoon season of 2020.

Analysis of remaining useful life of slope based on nonlinear wiener process

A remaining useful life (RUL) prediction model based on the nonlinear Wiener process is proposed to better tackle the life evaluation problem in the slope degradation process. Taking the displacement of the slope as its performance degradation index, and the nonlinear Wiener process is used to establish the RUL prediction model of the slope. For this model, the least squares method (LSM) is used to estimate the drift coefficients, the maximum likelihood estimation method (MLEM) is used to estimate the diffusion parameters, and then the probability density function (PDF) of the RUL of the slope is deduced and the RUL is predicted. The proposed model is verified by slope engineering examples. The results demonstrated that the RUL of the degradation model based on the nonlinear Wiener process has a greater prediction accuracy than the linear Wiener process. Because the various nonlinear functions have varying slope adaptations, and it can predict the RUL of a slope more accurately, which can provide more reliable preventive maintenance decisions.

A novel flexible exponent power-X family of distributions with applications to COVID-19 mortality rate in Mexico and Canada.

This paper aims to introduce a novel family of probability distributions by the well-known method of the T-X family of distributions. The proposed family is called a "Novel Generalized Exponent Power X Family" of distributions. A three-parameters special sub-model of the proposed method is derived and named a "Novel Generalized Exponent Power Weibull" distribution (NGEP-Wei for short). For the proposed family, some statistical properties are derived including the hazard rate function, moments, moment generating function, order statistics, residual life, and reverse residual life. The well-known method of estimation, the maximum likelihood estimation method is used for estimating the model parameters. Besides, a comprehensive Monte Carlo simulation study is conducted to assess the efficacy of this estimation method. Finally, the model selection criterion such as Akaike information criterion (AINC), the correct information criterion (CINC), the Bayesian information criterion (BINC), the Hannan-Quinn information criterion (HQINC), the Cramer-von-Misses (CRMI), and the ANDA (Anderson-Darling) are used for comparison purpose. The comparison of the NGEP-Wei with other rival distributions is made by Two COVID-19 data sets. In terms of performance, we show that the proposed method outperforms the other competing methods included in this study.

Likelihood function derivatives for a linear mixed model with compound symmetry assumption

The paper explores the properties of linear mixed models with simple random effects of the form: yi = Xiβ + ZiYi + εi, i = 1, . . . ,M, Yi ∼ N(0, Ψ), εi ∼ Т(0, σ2I), where M is the number of distinct groups, each consisting of ni observations. Random effects Yi and within-group errors εi are independent across different groups and within the same group. β is a p-dimensional vector of fixed effects, Yi is a q-dimensional vector of random effects, and Xi and Zi are known design matrices of dimensions nixp and nixq, of fixed and random effects respectively. Vectors εi represent within-group errors with a spherically Gaussian distribution.Assuming a compound symmetry in the correlation structure of the matrix Ψ governing the dependence among within-group errors, analytical formulas for the first two partial derivatives of the profile restricted maximum likelihood function with respect to the correlation parameters of the model are derived. The analytical representation of derivatives facilitates the effective utilization of numerical algorithms like Newton-Raphson or Levenberg-Marquardt.The restricted maximum likelihood (REML) estimation is a statistical technique employed to estimate the parameters within a mixed-effects model, particularly in the realm of linear mixed models. It serves as an extension of the maximum likelihood estimation method, aiming to furnish unbiased and efficient parameter estimates, especially in scenarios involving correlated data. Within the framework of the REML approach, the likelihood function undergoes adjustments to remove the nuisance parameters linked to fixed effects. This modification contributes to enhancing the efficiency of parameter estimation, particularly in situations where the primary focus is on estimating variance components or when the model encompasses both fixed and random effects.

A pathway study of factors influencing quality of fertility life

BackgroudTo investigate the factors influencing fertility quality of life in infertile men, constructing a structural equation model of the factors influencing fertility quality of life in infertile men, and to provide suggested measures for improving fertility quality of life in infertile men.MethodsIt is a Observational study. Infertile men (n = 250) attending a fertility centre in a hospital in Xinjiang, matched 1:2 men with no obvious male factor in the control group (n = 500).The Quality of Fertility Life Scale, the Social Support Scale, the Fertility Stress Scale and the Positive Attention Awareness Scale were used to conduct the survey. The model was constructed by applying the maximum likelihood estimation method in Mplus 8.3 software, to explore the factors influencing the quality of reproductive life of infertile men through path analyses. Differences between the case and control groups were statistically significant (P < 0.05) in terms of total fertility quality of life scores, core entry dimensions, affective responses, physical and mental relationships, selective treatment dimensions, and treatment tolerance.ResultsPast medical history, history of exposure to hazardous environments, health insurance reimbursement, social support, fertility stress, and mindfulness are important factors affecting the quality of fertility life of infertile men.ConclusionThe quality of fertility life of infertile men is not optimistic. By improving the level of mindfulness, fertility stress, and social support, we propose appropriate measures to improve the quality of fertility life of infertile men. These measures can improve their confidence in clinical diagnosis and infertility treatment, enabling them to cope positively with these challenges.

Discovering Subgroups of Children With High Mortality in Urban Guinea-Bissau: Exploratory and Validation Cohort Study.

The decline in global child mortality is an important public health achievement, yet child mortality remains disproportionally high in many low-income countries like Guinea-Bissau. The persisting high mortality rates necessitate targeted research to identify vulnerable subgroups of children and formulate effective interventions. This study aimed to discover subgroups of children at an elevated risk of mortality in the urban setting of Bissau, Guinea-Bissau, West Africa. By identifying these groups, we intend to provide a foundation for developing targeted health interventions and inform public health policy. We used data from the health and demographic surveillance site, Bandim Health Project, covering 2003 to 2019. We identified baseline variables recorded before children reached the age of 6 weeks. The focus was on determining factors consistently linked with increased mortality up to the age of 3 years. Our multifaceted methodological approach incorporated spatial analysis for visualizing geographical variations in mortality risk, causally adjusted regression analysis to single out specific risk factors, and machine learning techniques for identifying clusters of multifactorial risk factors. To ensure robustness and validity, we divided the data set temporally, assessing the persistence of identified subgroups over different periods. The reassessment of mortality risk used the targeted maximum likelihood estimation (TMLE) method to achieve more robust causal modeling. We analyzed data from 21,005 children. The mortality risk (6 weeks to 3 years of age) was 5.2% (95% CI 4.8%-5.6%) for children born between 2003 and 2011, and 2.9% (95% CI 2.5%-3.3%) for children born between 2012 and 2016. Our findings revealed 3 distinct high-risk subgroups with notably higher mortality rates, children residing in a specific urban area (adjusted mortality risk difference of 3.4%, 95% CI 0.3%-6.5%), children born to mothers with no prenatal consultations (adjusted mortality risk difference of 5.8%, 95% CI 2.6%-8.9%), and children from polygamous families born during the dry season (adjusted mortality risk difference of 1.7%, 95% CI 0.4%-2.9%). These subgroups, though small, showed a consistent pattern of higher mortality risk over time. Common social and economic factors were linked to a larger share of the total child deaths. The study's results underscore the need for targeted interventions to address the specific risks faced by these identified high-risk subgroups. These interventions should be designed to work to complement broader public health strategies, creating a comprehensive approach to reducing child mortality. We suggest future research that focuses on developing, testing, and comparing targeted intervention strategies unraveling the proposed hypotheses found in this study. The ultimate aim is to optimize health outcomes for all children in high-mortality settings, leveraging a strategic mix of targeted and general health interventions to address the varied needs of different child subgroups.

The modified control charts for monitoring the error detection of process control under different estimators&amp;nbsp;

The reflected power function distribution (RPFD) has increasing importance in practical life due to its application in diversified fields of life. Organisations often face difficulty monitoring operations to identify and remove errors during production. That is why there is a need to introduce control charts that effectively monitor the processes, mainly when the number of errors follows RPFD and the manufacturing process is in control. The current study suggested memory-based control charts as a solution to the problem. The control charts are based on the estimation methods and play a remarkable role in enhancing the machine process reliability. The parameters of RPFD are evaluated through the percentile estimator (PE) and modified maximum likelihood estimator methods (MMLM). Further, we create memory-based control charts, i.e., hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA), using the PE and MMLM. The findings reflect that HEWMA control charts based on PE provide a better result in estimating the defects. The implications of the study will be helpful for practitioners and policy makers from reliability engineering, management sciences, and statisticians.

EZ-CDM: Fast, simple, robust, and accurate estimation of circular diffusion model parameters.

The investigation of cognitive processes that form the basis of decision-making in paradigms involving continuous outcomes has gained the interest of modeling researchers who aim to develop a dynamic decision theory that accounts for both speed and accuracy. One of the most important of these continuous models is the circular diffusion model (CDM, Smith. Psychological Review, 123(4), 425. 2016), which posits a noisy accumulation process mathematically described as a stochastic two-dimensional Wiener process inside a disk. Despite the considerable benefits of this model, its mathematical intricacy has limited its utilization among scholars. Here, we propose a straightforward and user-friendly method for estimating the CDM parameters and fitting the model to continuous-scale data using simple formulas that can be readily computed and do not require theoretical knowledge of model fitting or extensive programming. Notwithstanding its simplicity, we demonstrate that the aforementioned method performs with a level of accuracy that is comparable to that of the maximum likelihood estimation method. Furthermore, a robust version of the method is presented, which maintains its simplicity while exhibiting a high degree of resistance to contaminant responses. Additionally, we show that the approach is capable of reliably measuring the key parameters of the CDM, even when these values are subject to across-trial variability. Finally, we demonstrate the practical application of the method on experimental data. Specifically, an illustrative example is presented wherein the method is employed along with estimating the probability of guessing. It is hoped that the straightforward methodology presented here will, on the one hand, help narrow the divide between theoretical constructs and empirical observations on continuous response tasks and, on the other hand, inspire cognitive psychology researchers to shift their laboratory investigations towards continuous response paradigms.

A Reliable Observation Point Selection Method for GB-SAR in Low-Coherence Areas

Ground-Based Synthetic Aperture Radar (GB-SAR), due to its high precision, high resolution, and real-time capabilities, is widely used in the detection of slope deformations. However, the weak scattering coefficient in low-coherence areas poses a great challenge to the observation point selection accuracy. This paper introduces a selection process for reliable observation points that integrates phase and spatial information. First, for various observation points with differentiated stability, we propose to utilize maximum likelihood estimation (MLE) methods to achieve stability assessment. Second, a phase correction approach is proposed to address unwrapped phase errors encountered at less stable points. Third, adaptive filtering for deformation information at observation points is achieved using estimated variance combined with wavelet filtering thresholds. Finally, in dealing with unknown deformation trends, we propose utilizing a clustering method to accurately identify these trends, thereby enhancing the precision in identifying reliable observation points (ROPs). The experimental results demonstrate that this method enhances the accuracy of observation point selection in low-coherence areas, providing a broader observational field for deformation detection.

The link between functional response and longevity of Trichogramma evanescens strains indigenous to Türkiye: A comparative assessment of parameters

AbstractA previous comprehensive survey in the Mediterranean and Southeastern regions of Türkiye investigating the natural egg parasitism of lepidopteran maize pests, Sesamia spp, (Lepidoptera: Noctuidae) Ostrinia nubilalis Hbn. and Chilo partellus (Swinhoe; Lepidoptera: Crambidae) by Trichogramma evanescens Westwood (Hymenoptera: Trichogrammatidae) yielded successful establishment of laboratory cultures of six strains molecularly clustering into two main groups. In this study, the functional response and adult longevity of the strains reared and tested on a factitious host, Ephestia kuehniella Zeller (Lepidoptera: Pyralidae) were investigated to provide insights into their potential as candidate biocontrol agents under constant laboratory conditions. The functional response modelling process consisted of two main sequential steps: model selection using polynomial logistic regression and parameter estimation using an iterative maximum likelihood estimation method. The functional response of two strains showed negative linear parameters (type II): HAP068M and HAP268S. Although their attack rate did not differ, the handling time of HAP268S was longer than that of HAP068M. In contrast, four strains had positive linear and negative quadratic parameters (type III) in their functional response: HAP044S, HAP070S, HAP210S, and HAP258M. The strains exhibiting type III functional response did not differ in their handling time, while HAP044S had a higher attack coefficient than HAP070S, HAP210S, and HAP258M. The longevity of both female and male adults significantly differed between strains. More importantly, the females belonging to strains exhibiting type II functional response presented a shorter longevity, compared to those with type III functional response. Males also showed a similar trend in their longevity. This paper discusses the differences in functional response types and estimated parameters of the strains in relation to their relevance for biological control programs and reveals a link between their functional response and longevity as potential reciprocal predictors.

Cross-Cultural Adaptation and Validation of the Portuguese Version of the Multidimensional Scale of Dating Violence 2.0 in Young University Students.

Dating violence has become a problem of social relevance with short- and long-term health consequences. Nurses are in a privileged position to detect and address this problem in health facilities and as school nurses in schools, providing health education and detecting this violence correctly. The aim of this study was to evaluate the cross-cultural validation of the Portuguese version of the Multidimensional Scale of Dating Violence-Short (MSDV 2.0). A validation investigation was carried out in two phases: (1) cross-cultural adaptation of the items and content validation of the Portuguese version of MSDV 2.0 and (2) psychometric validation. Phase (1): The items of the original version include a cross-cultural translation from Spanish to Portuguese and analysed by a group of experts in gender violence and by the authors of the original scale, then a back translation was made and again reviewed by the experts. Young university students also participated for face validity, and a pilot test was carried out. Phase (2): Confirmatory factor analysis was performed using the robust maximum-likelihood estimation method, which confirmed the five-dimensional structure, obtaining good fit rates (chi-square significance (χ2) = 187.860 (p < 0.0001); root mean square error of approximation (RMSEA) = 0.049; comparative fit index (CFI) = 0.937; Tucker-Lewis index (TLI) = 0.923). Reliability analysis indicated adequate internal consistency (Cronbach's alpha (α) = 0.88 to 0.70). Finally, scores of the Portuguese versions MSDV 2.0 were correlated, as expected, positively with the Depression, Anxiety, and Stress Scale (DASS-21) (r = 0.36 to 0.16) and negatively with the Medical Outcomes Study Questionnaire Short Form 36, Health Survey (SF-36) (r = -0.30 to -0.14). To date, it is the only instrument that measures dating violence in a multidimensional way validated in the Portuguese university context.

Predicting affective and cognitive learning outcomes: A quantitative analysis using climate change vectors

Recent changes in the atmospheric conditions have exerted a lot of pressure on the surface of the earth causing attitudinal change, fear of survival as well as pattern of living. Schools are not out of these influences from the changes in climatic conditions. These study, therefore. examines the nexus between climate change vectors such as classroom temperature variation, persistent drought, severe flood occurrence on class attendance, class participation and academic performance among secondary school students. The study adopted an ex post facto research design, and a total of 1,881 were used for data collection. Two research instruments, the climate change variation scale and class attendance, class participation, and academic performance scale were used for data collection. The instrument was validated using factor analysis to assess the dimensionality of the items as well as obtain factors using component analysis and varimax rotation. To assess principal the mode fitness and acceptability, the confirmatory factor analysis (CFA) was carried out using the maximum likelihood estimation method, and the factor loadings from exploratory factor analysis and CFA were not too different. The collected data were analyzed using the simple and multilinear regression techniques. The results showed that relatively, persistent, severe flooding and classroom temperature variation contributes significantly to class participation, class attendance, and academic performance among students. Similarly, the variables; severe flood, drought and classroom temperature when compositely examined contributes to the variation in class attendance, class participation and academic performance among students. Implications and recommendations of the study were stated.

Modeling rainfall extremes along the coastal and Northern parts of Ghana

The main objective of the study was to determine the appropriate distribution for extreme rainfall along the coastal and northern sectors of Ghana. For stakeholders and policymakers to make appropriate risk-mitigating measures to lessen the damage caused by flood and drought, it is necessary to make proper inferences about extreme rainfall. In this study, we used both the multivariate and univariate extreme value data analysis approaches. The Generalized Extreme Value (GEV) with the Block Maxima approach and Generalized Pareto Distribution (GPD) with the Peak over the threshold (that is all excesses and decluster peaks approaches) were used in this study. Historical gridded monthly maximum rainfall data from 1970 to 2020 were obtained from the Climatic Research Unit and were grouped as the coastal and northern stations. The Maximum Likelihood Estimation method was used to estimate the model parameters, and both the unit root test and the Mann-Kendall tests were used to test for trend in the data. With the multivariate extreme modelling approach, the logistic bivariate GEV model was chosen as the “best” model. However, the dependence value was 0.965, so the extreme rainfall should be modelled independently using the univariate extreme value approaches. Hence, based on the information criteria and analysis of deviance approaches, the GEV distribution was considered the “best” fit for the extreme rainfall dataset for the northern part of Ghana. In contrast, the GPD distribution was the “best” fit for the coastal station. Comparatively, for the volume of rainfall in the year 2020, the extreme rainfall is expected to be higher in the coastal station of Ghana in the next two years. Also, extreme rainfall in 2 years would not exceed the maximum occurrence of rainfall (279.267), which happened in September 2020 at the northern station of Ghana.

Birnbaum Saunders distribution for imprecise data: statistical properties, estimation methods, and real life applications

A neutrosophic statistic is a random variable and it has a neutrosophic probability distribution. So, in this paper, we introduce the new neutrosophic Birnbaum–Saunders distribution. Some statistical properties are derived, using Mathematica 13.1.1 and R-Studio Software. Two different estimation methods for parameters estimation are introduced for new distribution: maximum likelihood estimation method and Bayesian estimation method. A Monte-Carlo simulation study is used to investigate the behavior of parameters estimates of new distribution, compare the performance of different estimates, and compare between our distribution and the classical version of Birnbaum–Saunders. Finally, study the validity of our new distribution in real life.