Maximum Likelihood Method Research Articles

Analysis of Reliability for the Electrical Industries Company in Diyala using Modified Extension Weibull Distribution (An Application and Simulation study)

In this paper defining modified extension Weibull distribution, reliability function and hazerd function, we explain the maximum likelihood method under type one censoring sample. The censored samples play an important role in reliability analysis .In this paper we estimate and derived modified extension Weibull distribution whith three parameters under the censored samples type one by maximum likelihood estimation method depend on Newton-Raphson method. Then we applied simulation procedure using Monte-Carlo technique to estimate reliability function under different samples sizes and various initial values for the parameters for all estimated parameters of modified extension Weibull model by used MATLAB program. Finally we find the probability density function f(t), reliability function R(t),and hazard function h(t) for real data which get it from (Diyala province Company) is one of the formations of the Ministry of Industry and Minerals. Paper type: Research paper

Construction and Validation of a Survey on the Technological Difficulties in Italian Secondary Schools: The Mathematics Teacher Case

(1) Background: This study explores the technological difficulties of mathematics teachers in Italian secondary schools, focusing on the factors that influence their ability to integrate technology in teaching. (2) Methods: A questionnaire was developed and administered to a pilot group of 45 mathematics teachers from vocational secondary schools in Sicily and Veneto, followed by a larger survey with 557 mathematics teachers across Italy. The structural model was analysed using the maximum likelihood method via AMOS software (v.22 SPSS Inc., Chicago, IL, USA). (3) Results: The results highlight the importance of personal commitment in the school context and students’ problem-solving skills as key factors influencing the teachers’ technological challenges. The findings also indicate dissatisfaction with the school institution and families, as well as personal resistance to using information and communication technologies (ICT) in more advanced educational activities. (4) Conclusions: The study underscores the significant impact of these technological difficulties on teachers’ effectiveness in fostering students’ problem-solving abilities, calling attention to the need for better institutional support and strategies to reduce resistance to ICT use in education.

Data-driven Approximation of Cumulative Distribution Function Using Particle Swarm Optimization based Finite Mixtures of Logistic Distribution

This paper proposes a data-driven approximation of the Cumulative Distribution Function using the Finite Mixtures of the Cumulative Distribution Function of Logistic distribution. Since it is not possible to solve the logistic mixture model using the Maximum likelihood method, the mixture model is modeled to approximate the empirical cumulative distribution function using the computational intelligence algorithms. The Probability Density Function is obtained by differentiating the estimate of the Cumulative Distribution Function. The proposed technique estimates the Cumulative Distribution Function of different benchmark distributions. Also, the performance of the proposed technique is compared with the state-of-the-art kernel density estimator and the Gaussian Mixture Model. Experimental results on κ−μ distribution show that the proposed technique performs equally well in estimating the probability density function. In contrast, the proposed technique outperforms in estimating the cumulative distribution function. Also, it is evident from the experimental results that the proposed technique outperforms the state-of-the-art Gaussian Mixture model and kernel density estimation techniques with less training data.

A Generalized Suja Distribution with Application to Lifetime Data

This paper introduces a generalized Suja distribution called the Kumaraswamy-Suja (KW-Suja) distribution using the Kumaraswamy generator. The proposed distribution has Suja distribution as a special case. Some statistical and reliability properties of the new distribution were derived and the method of maximum likelihood was employed for estimating the model parameters. The usefulness and flexibility of the KW-Suja distribution were illustrated with a real lifetime data. Results based on the log-likelihood and goodness of fit statistics values showed that the KW-Suja distribution provides a better fit to the data than the other competing distributions considered in this study. The KW-Suja distribution is therefore recommended for effective modelling of the unimodal or bimodal continuous lifetime data with non-decreasing shape and bathtub-shaped failure rate.

The risk factors determined by four machine learning methods for the change of difference of bone mineral density in post-menopausal women after three years follow-up

The prevalence of osteoporosis has drastically increased recently. It is not only the most frequent but is also a major global public health problem due to its high morbidity. There are many risk factors associated with osteoporosis were identified. However, most studies have used the traditional multiple linear regression (MLR) to explore their relationships. Recently, machine learning (Mach-L) has become a new modality for data analysis because it enables machine to learn from past data or experiences without being explicitly programmed and could capture nonlinear relationships better. These methods have the potential to outperform conventional MLR in disease prediction. In the present study, we enrolled a Chinese post-menopause cohort followed up for 4 years. The difference of T-score (δ-T score) was the dependent variable. Information such as demographic, biochemistry and life styles were the independent variables. Our goals were: (1) Compare the prediction accuracy between Mach-L and traditional MLR for δ-T score. (2) Rank the importance of risk factors (independent variables) for prediction of δ T-score. Totally, there were 1698 postmenopausal women were enrolled from MJ Health Database. Four different Mach-L methods namely, Random forest (RF), eXtreme Gradient Boosting (XGBoost), Naïve Bayes (NB), and stochastic gradient boosting (SGB), to construct predictive models for predicting δ-BMD after four years follow-up. The dataset was then randomly divided into an 80% training dataset for model building and a 20% testing dataset for model testing. A 10-fold cross-validation technique for hyperparameter tuning was used. The model with the lowest root mean square error for the validation dataset was viewed as the best model for each ML method. The averaged metrics of the RF, SGB, NB, and XGBoost models were used to compare the model performance of the benchmark MLR model that used the same training and testing dataset as the Mach-L methods. We defined that the priority demonstrated in each model ranked 1 as the most critical risk factor and 22 as the last selected risk factor. For Pearson correlation, age, education, BMI, HDL-C, and TSH were positively and plasma calcium level, and baseline T-score were negatively correlated with δ-T score. All four Mach-L methods yielded lower prediction errors than the MLR method and were all convincing Mach-L models. From our results, it could be noted that education level is the most important factor for δ-T Score, followed by DBP, smoking, SBP, UA, age, and LDL-C. All four Mach-L outperformed traditional MLR. By using Mach-L, the most important six risk factors were selected which are, from the most important to the least: DBP, SBP, UA, education level, TG and sleeping hour. δ T score was positively related to SBP, education level, UA and TG and negatively related to DBP and sleeping hour in postmenopausal Chinese women.

Reliability Estimation of Scale Parameter in Type II Generalized Half-Logistic Distribution from Doubly Censored Samples Based on Monte Carlo Simulation

Objectives: This article deals with estimation of the reliability function for one-parameter Type II Generalized Half- Logistic distribution (Type II GHLD). Methods: The Maximum likelihood (ML) and Approximate Maximum likelihood (AML) methods provided by Jilani et.al. 1 . Findings: Comparisons between the estimators were made using Monte Carlo Simulation based on statistical indicter bias and mean squared error (MSE). We have generated 3000 random samples of size n=10(5)20 from a standard one-parameter Type II GHLD with = 0.5, 1.5 and 2.0. Each sample is then ordered and from this sample a doubly (including left and right) censored sample is considered, by censoring r smallest observations and s largest observations with all possible choices of r and s corresponding to this resultant sample we compute MLEs (using Newton-Raphson method), the LAMLE and unbiased LAMLE . Finally, the results are explained with tables. Novelty: This study has empirically proves that all the three reliability estimators have the same asymptotic variance. Hence, in this case, any one of the three estimators can be used but preferable estimator based unbiased estimator. Keywords: Maximum likelihood estimation, Approximate Maximum likelihood estimation, Bias, Mean squared error, Variances

Parameter estimation of three-parameter Weibull distribution by hybrid gray genetic algorithm with modified maximum likelihood method with small samples

Parameter estimation of three-parameter Weibull distribution by hybrid gray genetic algorithm with modified maximum likelihood method with small samples

Genome-Wide Identification of the Geranylgeranyl Pyrophosphate Synthase (GGPS) Gene Family Associated with Natural Rubber Synthesis in Taraxacum kok-saghyz L. Rodin.

Taraxacum kok-saghyz Rodin (TKS) is a recognized alternative source of natural rubber comparable to the rubber tree. The geranylgeranyl pyrophosphate synthase (GGPS) catalyzed the synthesis of geranylgeranyl pyrophosphate (GGPP), which is an important enzyme in the secondary metabolism pathway. In this study, we present the first analysis of the GGPS gene family in TKS, where a total of seven TkGGPS family members were identified. Their core motifs, conserved structural domains, gene structures, and cis-acting elements were described. In addition, two phylogenetic trees were constructed based on the Neighbor-Joining and Maximum-Likelihood methods, and the TkGGPSs were highly conserved and exhibited good collinearity with the other species. Transcriptome data showed that seven TkGGPS gene members were expressed in all the 12 tissues measured, and TkGGPS1, TkGGPS3, and TkGGPS6 were highly expressed in latex, suggesting that they may be associated with natural rubber synthesis. Meanwhile, quantitative real-time PCR (qRT-PCR) showed that the expression levels of the TkGGPS genes were regulated by the ethylene and methyl jasmonate (MeJA) pathways. Subcellular localization results indicated that all the TkGGPS proteins were also located in chloroplasts involved in photosynthesis in plants. This study will provide valuable insights into the selection of candidate genes for molecular breeding and natural rubber biosynthesis in TKS.

Significance of different probability distributions in flood frequency analysis of Brahmani-Baitarani River Basin, India

Appropriate flood management in a basin requires analysis of peak discharge prediction and flood frequency. The main aim is to find the most suitable distribution model at various gauges for the entire Brahmani-Baitarani River basin for proper flood management. Daily flow data lengths ranging from 23 to 46 years for multiple gauges are obtained from the Central Water Commission. The present analysis employs the Generalized Extreme Value (GEV), Gumbel Max, Log-Pearson III (LP3), and Lognormal models to estimate the flood quantiles of various return periods. The L-moment, Method of Moment, and Maximum Likelihood Method are applied to estimate the model parameters. Goodness-of-fit tests, accuracy measures, and relative scoring indicated LP3 as the best-fit model, followed by GEV. The results indicated that floods with return periods of longer than 100 years can be considered for designing hydraulic structures in the upper reaches of the basin, whereas floods with return periods of longer than 50 years can be considered for the lower reaches. Significant constraints in the present study involve a limited number of gauges and their varied record lengths in this extensive basin. The findings of this study can be used in water resource planning, flood hazard mapping, and the design of hydraulic structures within similar catchments.

A bivariate dependent degradation model based on artificial neural network supported stochastic process and Copula function

AbstractIn order to use the high ability of the artificial neural network (ANN) in data fitting, this paper introduces an ANN in stochastic process to describe the mean function for degradation modeling. Due to the fact that the existing method cannot handle the bivariate dependent degradation conditions, a bivariate dependent degradation model based on Copula function and ANN‐supported stochastic processes is proposed. Considering the random effects caused by individual difference, it is assumed that the unknown parameters in the stochastic processes and Copula functions are randomly distributed. Based on the maximum likelihood and moment estimation methods, a related statistical inference method for ANN training and parameter estimation is developed to use the bivariate dependent degradation model. An actual fatigue crack dataset is used to demonstrate the validity of the proposed method. The obtained results show that the dependent relationship between two degradation indicators should not be neglected, and it can be efficiently handled by the proposed method. Furthermore, the proposed degradation model can provide reliability and degradation intervals with enough precision due to the fact that it considers the random effects caused by individual difference.

Surat’s sustainable future: analyzing compact urban development and population density trends

Rapid urbanization is a challenge for the cities of developing countries like India. The share of an urban area is rapidly increasing in dynamically growing cities. Due to this, the land use is altered, causing sprawl and unplanned development. The consumption of resources is greater, and the impact on the surroundings is negative. The compact city concept is always more efficient and cost effective compared to unplanned organic growth. The compact city optimizes available land resources with its maximum possible capacity in accordance with other available natural resources. The primary study objective is to assess the growth trend of Surat city using satellite images, geographic information system techniques, and census data for the last few years. The analysis considers population density for different city wards from 1991 to 2020. Based on the land use land cover change carried out using the maximum likelihood method from the satellite images, the rate of spreading out, its direction, and causes are also found. In this study, population density is a crucial attribute of the compact city concept. The study shows that wardwise density is increasing in a specific direction and making that portion of the city a dense, compact development. This is observed in ward numbers 48, 42, and 35 in the east, north, and southeast directions from Central Business District, respectively. The average population density in persons per sq. km is continuously increasing from 5006 to 20329 at city level which also shows the compact city development for Surat. The governing authorities must incorporate the compact city concept into the planning policy for sustainable urban development. By this, policymakers can understand housing needs to promote affordable housing, invest in infrastructure development and public services, and identify areas where sustainable transportation options, such as public transit, walking, or cycling, need improvement.

Optimization design of composite cap-shape pillar structure based on gaussian process of combined kernel function

Abstract To quickly realize the optimal design of the cap-shaped structure, an optimization design method of composite cap-shaped pillar structure based on combined kernel function Gaussian process was proposed. First, the shortcomings of two kernel functions representing different linear characteristics of data in model construction were analyzed, on which a new combined kernel function was constructed. Based on the finite element numerical simulation results, a database with the web thickness, web height, fiber volume, and ultimate bearing capacity of the cap-shaped structure was constructed. Then, a Gaussian process model based on the combined kernel function was established and the model parameters were trained by the maximum likelihood method. Finally, taking the ultimate bearing capacity per unit volume as the optimization objective, the artificial fish swarm algorithm was used to quickly obtain the structure design parameters under the optimal objective function, and the simulation results were compared with the initial design parameters. The results showed that the method proposed in this paper can optimize the structure performance, improve the design efficiency, and meet the engineering design requirements.

The Complete Mitochondrial Genomes of Five Nivanini Species (Hemiptera: Cicadellidae: Evacanthinae) With Phylogenetic Analysis.

To delve deeper into the phylogenetic relationships within Cicadellidae and the taxonomic arrangement of Evacanthinae, our study focuses on the mitochondrial genome sequencing of five Nivanini species: Extensus latus, Concavepiana hamulusa, Sophonia nigrilineata, Sophonia microstaina, and Sophonia fuscomarginata. The results showed that the length of the five mitochondrial genomes ranged from 15,610 to 16,032 bp and included 37 typical genes. The A + T content of Nivanini ranged from 72.5% to 78.7%, which is consistent with that of other sequenced Evacanthinae species. All transfer RNAs (tRNAs) exhibit the typical cloverleaf secondary structure, except for trnS (AGY), which lacks the dihydrouracil (DHU) arm. With regard to protein-coding genes, all started with ATN codons, except for atp8, and most of them use TAA or TAG as termination codons. Using the Bayesian inference and maximum likelihood methods, a phylogenetic tree based on all 37 genes was constructed, with a total of 57 Cicadellidae species and two outgroups included as research objects. The analyses confirmed the monophyletic nature of each subfamily, highlighting Deltocephalinae as the oldest, distinctively parallel to the others.

The Rediscovery of Noblella peruviana after More than 115 Years Helps Resolve the Molecular Phylogeny and Taxonomy of Noblella (Amphibia, Anura, Strabomantidae)

We revise the taxonomy of the frog genus Noblella on the basis of a molecular phylogeny. Previous studies recognized that Noblella is non-monophyletic, with one clade distributed from southeastern Peru to northeastern Bolivia and adjacent areas in Brazil and another clade distributed from northern Peru to Ecuador and southeastern Colombia. The lack of sequences from the type species Noblella peruviana prevented the investigation of its phylogenetic position and the status of related taxa. Our rediscovery after more than 115 years allowed for the inclusion of DNA sequences of Noblella peruviana obtained from specimens collected at the type locality in southeastern Peru. We inferred a phylogeny based on a concatenated dataset (three mitochondrial and two nuclear loci) using Bayesian and maximum likelihood methods. Our phylogeny corroborated the non-monophyly of Noblella and helped resolve the status of related taxa, including Psychrophrynella bagrecito, the type species of the genus Psychrophrynella (rediscovered after 42 years). We identified a clade containing N. peruviana, P. bagrecito, and other species of Noblella and Psychrophrynella distributed in southern Peru. Given that the name Noblella predates Psychrophrynella, we propose that Psychrophrynella should be considered a junior synonym of Noblella. The second clade contains species of Noblella distributed in Ecuador and northern Peru, including N. myrmecoides, which used to be the type species of the genus Phyllonastes. Consequently, we propose to reinstate the genus Phyllonastes to accommodate all species of Noblella distributed in Ecuador, northern Peru, southeastern Colombia, and adjacent areas in Brazil. We present an updated taxonomy including new combinations for 12 species and reinstatements for three species.

Sychnotylenchus kulinichi sp. n. (Nematoda: Anguinoidea) from the Primorsky Krai of Russia with a tabular key to the genus Sychnotylenchus Rühm, 1956

Summary A new species of the genus Sychnotylenchus Rühm, 1956, S. kulinchi sp. n., inhabiting the bark beetle galleries of Pityogenes chalcographus in Pinus koraiensis was found in the Primorsky Krai of Russia. The new species differs morphologically from the closely related species S. yasinskii and S. mayor in having a shorter body length (626-1030 vs 1250-1280 and 1935-1455 μm, respectively) and from S. sparnugus in having a greater value of the ratio between spicule length and tail length (0.9-11 vs less than 0.7). Phylogenetic analysis of the partial 18S rRNA, D2-D3 expansion segments of the 28S rRNA, the ITS rRNA and COI gene sequences showed that the Russian S. kulinichi sp. n. population grouped with populations from Israel and an unspecified locality that were identified incorrectly as Ditylenchus forepolitor, which are considered conspecific with S. kulinichi sp. n. in this study. Phylogenetic analyses aiming to clarify the controversial taxonomic status of Neoditylenchus and Sychnotylenchus species indicated that, although the genus Sychnotylenchus was paraphyletic in some phylogenetic trees, testing of alternative topologies for the 18S rRNA, D2-D3 of 28S rRNA and ITS rRNA gene trees and datasets using the maximum likelihood method did not exclude the monophyly of this genus and did not justify the validity of the genus Neoditylenchus, which should be considered a junior synonym of Sychnotylenchus as proposed by Fortuner & Maggenti (1987). Molecular phylogeny showed close relationships of Sychnotylenchus with plant-parasitic nematodes from the genera Ficotylus, Orrina and Pterotylenchus, and also with the insect-associated genus Neomisticius. A polytomous key listing 24 morphological diagnostic characters for the identification of 33 species of Sychnotylenchus is provided, along with a table listing associated bark beetle species.

Molecular phylogenetic relationships among lineages in the genus Carabus (Coleoptera: Carabidae) and radiation of the subgenus Apotomopterus

Abstract The genus Carabus (Coleoptera: Carabidae: Carabinae) is a group of predacious ground beetles found throughout Holarctic temperate zones. The diversification of this group is attributed not only to allopatric speciation but also to diversification in life-history traits and morphological traits that are involved in ecological adaptation and reproductive isolation. Precise phylogenetic reconstruction of Carabus is important to understanding the factors associated with species’ divergence in relation to such character divergence. Here, we analyse the phylogeny of Carabus among higher taxonomic groups and among species of the subgenus Apotomopterus, a hyper-diverse group endemic to East Asia. We used genome-wide sequence data from ultraconserved elements for phylogenetic reconstruction via maximum-likelihood and species-tree reconstruction methods. With regard to the relationships among higher taxonomic groups, the obtained phylogenetic trees resolved two structures with previously unresolved divergence. The subgenus Apotomopterus contained three lineages, i.e. the Vitalisi, Prodigus, and Sauteri groups. It showed diversification of the spinula, a sclerotized male genital structure, and variation in the female elytral notch (preapical emargination). These morphological traits may be involved in copulatory behaviour and potentially affect reproductive isolation, and their character state divergence may have facilitated species divergence of Apotomopterus.

Role of Embolic Protection in Percutaneous Coronary Intervention without Saphenous Venous graft lesions in ST-elevation myocardial infarction - a systematic review and meta-analysis.

Embolic protection devices are catheter-based devices that can be used to capture atherosclerotic remnants released during percutaneous coronary intervention (PCI). We aim to study the efficacy and safety of EPDs in PCIs without saphenous vein grafts (SVG) in ST-elevation myocardial infarction(STEMI). 3 electronic databases of MEDLINE, Web of Science, and Embase were searched from inception to Apr 10, 2024, to identify relevant randomized controlled trials (RCTs) that compared outcomes of patients subjected to EPD during PCI with control group where EPDs were not utilized. The primary outcome was 30-day all-cause mortality. Secondary outcomes were major adverse cardiovascular and cerebrovascular events (MACCE) at 30 days, post-PCI Thrombolysis in Myocardial Infarction (TIMI) grade 3 flow attainment, ST-segment resolution at 90 minutes post-procedure and post-procedure angiographically detectable signs of distal embolization. The effect estimates of outcomes were assessed using risk ratio (RR) with a 95% confidence interval (CI). Random-effects meta-analysis was conducted using the restricted maximum likelihood method given the inter-study variance was inevitable. We included 3 RCTs enrolling 741 patients (age 61.6 ± 12.15 years, 22% females) undergoing PCI without SVG lesions. As opposed to the control group, the use of EPD did not yield a significant effect on all-cause mortality (RR, 0.76; 95% CI, 0.31-1.86; I2 = 0%), MACCE (RR, 0.66; 95% CI, 0.34-1.27; I2 = 0%), post-PCI TIMI 3 flow (RR, 1.18; 95% CI, 0.86-1.62; I2 = 77%) and ST segment resolution at 90 minutes post-procedure (RR, 1.05; 95% CI, 0.90-1.22; I2 = 0%). However, EPD significantly decreased angiographically detectable signs of distal embolization (RR, 0.60; 95% CI, 0.36 to 0.99; I2 = 0%). EPD significantly reduced angiographically detectable signs of distal embolization in PCI without SVG lesions in STEMI, though there were no clinical signs of improved flow or mortality. Further trials are necessary to thoroughly evaluate the potential benefits and requirements of EPD usage in such procedures.

Urea to Treat Hyponatremia Due to Syndrome of Inappropriate Antidiuretic Hormone Secretion: A Systematic Review and Meta-Analysis

Rationale & ObjectiveThe use of urea to treat hyponatremia related to the Syndrome of Inappropriate Antidiuretic Hormone Secretion (SIADH) has not been universally adopted due to questions about effectiveness, safety, and tolerability. This systematic review and meta-analysis of observational studies aimed to address these questions. Study DesignThis PRISMA-guided study examined published research across four electronic databases. Study PopulationsPatients with SIADH-related hyponatremia. Selection CriteriaClinical trials and observational studies reporting at least one outcome related to serum sodium concentration, symptom resolution, or adverse effects after oral or nasogastric urea administration. Data ExtractionData extraction was performed independently by two reviewers using a standardized form recording study characteristics, participant demographics, intervention details, and treatment outcomes. Analytical ApproachA meta-analysis was conducted using the restricted maximum likelihood method for the random-effects model to assess the effect of urea treatment on serum sodium and serum urea compared to other treatment modalities. Subgroup analyses were conducted based on treatment duration and SIADH severity. ResultsUrea treatment significantly increased serum sodium [mean difference (MD) = 9.08 (95%CI 7.64-10.52), p < 0.01] and urea [MD = 31.66 (95%CI 16.05-47.26), p < 0.01] in patients with SIADH albeit with significantly high heterogeneity. Subgroup analysis based on the treatment duration showed a significant rise in the serum sodium level after 24 hours, two, five, seven, and fourteen days, as well as after one year of treatment. Greater increases in serum sodium levels after treatment with urea occurred in patients with severe (<120 mEq/L) [MD = 18.04 (95%CI 13.68-22.39)] than with moderate (120-129 mEq/L [MD = 7.86 (95%CI 6.78-8.94)] or mild (130-135 mEq/L) [MD = 8.00 (95%CI 7.31-8.69)] SIADH induced hyponatremia. Urea treatment was comparable to fluid restriction [MD = 0.81 (95%CI: -0.93-2.55), p = 0.36) and vaptans [MD = -1.96 (95%CI: -4.59-0.66, p = 0.14) but superior to no treatment [MD = 7.99 (95%CI 6.25-9.72), p < 0.01]. Urea was associated with minor adverse events, with poor palatability being most common. LimitationsAs no RCTs investigating urea as a treatment for hyponatremia were identified for inclusion, these analyses were based on observational studies. ConclusionsUrea is safe and effective for managing SIADH-induced hyponatremia. These finding suggest that urea may be a useful treatment modality in resource-limited settings or when other treatments are contraindicated or poorly tolerated.

Parameter Estimation of the Inverted Kumaraswamy Distribution by Using L-Moments Method: An Application on Precipitation Data

Modeling precipitation data plays a critical role in water resource and flood management. Statistical distributions are frequently used in describing hydrological variables. Different distributions and estimation methods have been presented in previous studies for modeling precipitation data. In this study, the inverted Kumaraswamy distribution is considered for its advantageous properties, and the L-moments and maximum likelihood methods are employed in estimating the parameters of the inverted Kumaraswamy distribution. In the application part, the annual maximum monthly precipitations recorded in the Rize, Türkiye are modeled with the inverted Kumaraswamy distribution. To the best of the author’s knowledge, the L-moment method is considered for the first time to estimate the parameters of the inverted Kumaraswamy distribution. In addition, the efficiencies of the estimation methods are compared with a Monte-Carlo simulation study. For evaluating the performances of the estimation methods, the goodness of fit criteria including root mean square error, Kolmogorov Smirnov test, and coefficient of determination (R^2) are used in the application part of the study. The results show that for the data considered, the L-moments method yields more accurate results than the maximum likelihood method in estimating the parameters when the sample size is small. Accordingly, the corresponding distribution with L-moments estimations provides a better fit to precipitation data obtained from the Rize station.

The Gompertz Inverted Nadarajah-Haghighi (GoINH) Distribution Properties with Application to real data

Over the past years, many academics in mathematical statistics have introduced new continuous distributions to respond to real-world data growth, and this adaptability or flexibility has become essential to this development. In this study, a new distribution called Gompertz Inverted Nadarajah-Haghighi (GoINH) is proposed, according to the Gompertz family which is a new four-parameter probability distribution model. In addition, we will present a number of properties of the proposed distribution such as moment generating function, survival function, risk function, characteristic function, quantile function, pdf expansion, and ordered statistics which represent a few of the many mathematical and statistical features of the recently proposed model. The model parameters were also estimated using the maximum likelihood method. In the end, a practical application was carried out on real data, represented by failure times for 40 heavy-duty locomotive engines, and comparison with a number of new or known distributions to determine the efficiency of the distribution using a number of informatics criteria is using the R programming language.