Maximum Likelihood Estimation Technique Research Articles

Statistical inference and data analysis for inverted Kumaraswamy distribution based on maximum ranked set sampling with unequal samples

A very useful modification to ranked set sampling (RSS) that allows a larger set size without significantly increasing ranking errors is the maximum ranked set sampling with unequal samples (MRSSU) approach. This article covers the parameter estimation of the inverted Kumaraswamy distribution using MRSSU and RSS designs. The maximum likelihood and Bayesian estimation techniques are considered. The regarded Bayesian estimation technique is determined in the case of non-informative and informative priors represented by Jeffreys and gamma priors, respectively. Squared error and minimum expected are the two loss functions that are employed. We presented a simulation study to evaluate the performance of the recommended estimations using root mean squared error and relative bias. The Bayes point estimates were computed using the Metropolis–Hastings algorithm. Additional conclusions have been made based on actual geological data regarding the intervals between Kiama Blowhole’s 64 consecutive eruptions. Based on the same number of measured units, the results of simulation and real data analysis showed that MRSSU estimators performed much better than their RSS counterparts.

Evaluating the influence of information and communication technology and the BRICS in South African trade dynamics: a gravity model approach

PurposeThis study aims to assess how South African membership to the Brazil, Russia, India, China and South Africa (BRICS) has influenced its traded sector. It also evaluated information and communication technology (ICT) as an instrument for enhancing bilateral trade.Design/methodology/approachICT was captured from three perspectives: mobile technology, internet usage and fixed telephones. It was integrated into an augmented gravity equation as a trade cost. The study covered 27 years and 181 South African trading partners. Estimation was done using the Poisson pseudo maximum likelihood estimation technique and the implementation of exporter-year and importer-year fixed effects.FindingsIt was revealed that mobile phone and fixed telephone subscriptions improve import and export by 4.66% and 1.79%, respectively, while the internet penetration rate negates export and import by 13.4% and 5.89%, respectively. However, it further demonstrates that the internet penetration rate and fixed telephone subscription reduced the negative impact of distance by 7.26% and 1.15% for export. ICT performed better when South Africa only traded with the BRICS countries. The report also shows an encouraging BRICS effect on South African bilateral trade with the bloc.Practical implicationsThe study highlights that BRICS membership significantly boosts South Africa’s bilateral trade, which encourages new African memberships, while also emphasising the role of ICT in mitigating the negative impact of distance. Policymakers should enhance mobile phone and fixed telephone infrastructures to improve imports and exports, respectively, and strategically manage internet penetration to maximise the benefits of BRICS economic cooperation.Originality/valueThe study evaluated the influence of South Africa’s BRICS membership and how ICT variables interact with distance to mitigate its effects on trade. This provides a nuanced understanding of ICT’s unique impact on South Africa’s bilateral trade, offering valuable insights for policymakers to enhance trade performance and leverage BRICS economic cooperation effectively.

Impact of Ebola Virus Disease and ECOWAS Membership on Intra-Regional Trade in West Africa

The West African sub-region bore the brunt of the world's largest Ebola outbreak, significantly impacting the economic activities and trade shares of the affected countries. This study seeks to examine the repercussions of the Ebola Virus Disease (EVD) on the trade shares of affected countries and to explore the potential influence of ECOWAS membership on intra-regional trade in West Africa. Using the Poison Pseudo Maximum Likelihood (PPML) estimation technique, an analysis of the augmented gravity model of international trade was conducted. The findings indicate a two-fold reduction in the trade shares of affected countries with their intra-regional partners due to the Ebola Virus Disease. Additionally, with Mauritania expressing its desire to join the ECOWAS sub-region, there is a need to explore the impact of the Regional Economic Community on intra-regional trade. Furthermore, the study reveals that ECOWAS membership has the potential to double trade levels in West Africa. The findings also suggest that Mauritania stands to gain significant benefits from becoming a member of the ECOWAS. In conclusion, this study highlights the necessity for ECOWAS to proactively respond to disease outbreaks and underscores the importance of increased research investment. Moreover, it emphasizes the need for the ECOWAS to further improve infrastructure to facilitate intra-regional trade, especially in transportation.

New Bounded Probability Model: Properties, Estimation, and Applications

The article introduces a new unit distribution, an extension of Tiessier distribution, characterized by a versatile hazard function capable of adopting diverse shapes such as bathtub or N-shaped curves. An exploration of the fundamental properties of this distribution is undertaken, accompanied by the implementation of the maximum likelihood estimation technique and eleven alternative methods to approximate its parameters effectively. Through a simulation study, the article effectively demonstrates the precision of these parameter estimation methods, even when dealing with small sample sizes. Two datasets are employed to apply the novel distribution, subjecting it to a comprehensive evaluation against established models utilizing a range of model selection criteria and goodness of fit tests. Notably, the article illustrates that the performance of the new distribution surpasses that of existing models in effectively capturing data patterns. Beyond its empirical contributions, the article highlights the potential cross-disciplinary applications of the new distribution in many fields while concurrently advancing the realms of probability theory and statistical inferences.

Estimation and Analysis of Trigonometric Models under Bayesian Approach

In this study, we explore three innovative trigonometric models within the Bayesian framework, utilizing the inverse Weibull distribution as our foundation. These models—namely the Sine inverse Weibull, Cosine inverse Weibull, and Tan inverse Weibull—are crafted from distinct distribution families. We employ both maximum likelihood estimation and Markov Chain Monte Carlo (MCMC) simulation techniques to estimate parameters, drawing upon a comprehensive dataset. By scrutinizing posterior samples numerically and graphically, we evaluate the efficacy of our models, generating Bayes estimates for parameters, examining reliability and hazard functions, and establishing credible intervals. Furthermore, we assess the predictive capacity of all three models through posterior predictive checks. We also conduct comparative analyses, pitting our models against competing ones using real-world data. Notably, our results reveal that the proposed trio of models exhibit strikingly similar performance in terms of fitting the data.

Statistical Study of the Mechanical Behavior of the New Fiber from the Strelitzia Juncea Plant Fibers: Application in Ecological Yarns

ABSTRACT To develop efficient, durable, and eco-friendly natural fiber composites, this study examines the physical properties of Strelitzia Juncea (SJ) fiber for potential industrial use. The focus is on how gauge length affects mechanical properties of SJ fibers, aiming to manufacture textile yarns. Tensile tests were performed on SJ yarns of varying diameters (0.95, 1.26, and 1.76 mm). In addition, 150 fibers across five-gauge lengths (GL) from 10 to 50 mm gave a strength of 731 to 270 MPa and a Young’s modulus of 28 to 31 GPa, with statistical analysis applied to evaluate the data’s variability. Statistical techniques were applied to assess and quantify this dispersion. Results were analyzed using Weibull distributions with different probability indices, along with least squares (LS) and maximum likelihood (ML) estimation techniques. Furthermore, for each tensile strength characteristic, a one-factor analysis of variance (ANOVA) was performed across the five groups.

A Generalized Class of Exponentiated Modified Weibull Distribution With Applications

Abstract: In this paper, a new class of five parameter gamma-exponentiated or generalized modified Weibull (GEMW) distribution which includes exponential, Rayleigh, Weibull, modified Weibull, exponentiated Weibull, exponentiated exponential, exponentiated modified Weibull, exponentiated modified exponential, gamma-exponentiated exponential, gamma exponentiated Rayleigh, gamma-modified Weibull, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh and gamma-exponential distributions as special cases is proposed and studied. Mathematical properties of this new class of distributions including moments, mean deviations, Bonferroni and Lorenz curves, distribution of order statistics and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to real data sets presented in order to illustrate the usefulness of this new class of distributions and its sub-models.

Unveiling the royal road to happiness: the predictive role of psychological hardiness, mediated by vitality and materialistic values

ABSTRACT The quest for happiness is highly esteemed in every culture. Based on the theory of the positive activity model, the current study examined the role of psychological hardiness in happiness among youth. The study also investigated the parallel mediating role of vitality and materialistic values in the relationship between psychological hardiness and happiness. Data were collected from 414 youths selected through purposive sampling techniques. The variables of the study were measured through standardized instruments. Findings generated through structural equation modelling with the maximum likelihood estimation technique revealed that psychological hardiness was a significant predictor of happiness. Additionally, vitality and materialistic values partially mediated the relationship between psychological hardiness and happiness. The present study is one of the first to include vitality and materialistic values as a parallel intermediary mechanism to explain the relationship between psychological hardiness and happiness. Implications of the study are discussed in light of the study findings.

Inference Based on Sequential Order Statistics with Lindley Distribution

In this paper, we consider the problem of estimation of parameters of Lindley distribution based on sequential order statistics under conditional proportional hazard rate model. Maximum Likelihood and Bayesian estimation techniques are applied for estimating the unknown parameters. Markov Chain Monte Carlo method is implemented for obtaining the Bayes estimators. An intensive simulation study is carried out to assess the performance of different estimators discussed in this paper. A real data analysis is also performed for illustrative purposes.

Advanced Copula-Based Models for Type II Censored Data: Applications in Industrial and Medical Settings

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology’s applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients.

On the Poisson-transmuted exponential distribution and its application to frequency of claim in actuarial science

This study proposes a new discrete distribution in the mixed Poisson paradigm to obtain a distribution that provides a better fit to skewed and dispersed count observation with excess zero. The cubic transmutation map is used to extend the exponential distribution, and the obtained continuous distribution is assumed for the parameter of the Poisson distribution. Various moment-based properties of the new distribution are obtained. The Nelder-Mead algorithm provides the fastest convergence iteration under the maximum likelihood estimation technique. The shapes of the proposed new discrete distribution are similar to those of the mixing distribution. Frequencies of insurance claims from different countries are used to assess the performance of the new proposition (and its zero-inflated form). Results show that the new distribution outperforms other competing ones in most cases. It is also revealed that the natural form of the new distribution outperforms its zeroinflated version in many cases despite having observations with excess zero counts.

The Transformed MG-Extended Exponential Distribution: Properties and Applications

Our research paper introduces a newly developed probability distribution called the transformed MG-extended exponential (TMGEE) distribution. This distribution is derived from the exponential distribution using the modified Frechet approach, but it has a more adaptable hazard function and unique features that we have explained in detail. We conducted simulation studies using two methods: rejection sampling and inverse transform sampling, to produce summaries and show distributional properties. Moreover, we applied the TMGEE distribution to three real datasets from the health area to demonstrate its applicability. We used the maximum likelihood estimation technique to estimate the distribution’s parameters. Our results indicate that the TMGEE distribution provides a better fit for the three sets of data as compared to nine other commonly used probability distributions, including Weibull, exponential, and lognormal distributions.

Nonparametric mean and variance adaptive classification rule for high‐dimensional data with heteroscedastic variances

AbstractIn this study, we introduce an innovative methodology aimed at enhancing Fisher's Linear Discriminant Analysis (LDA) in the context of high‐dimensional data classification scenarios, specifically addressing situations where each feature exhibits distinct variances. Our approach leverages Nonparametric Maximum Likelihood Estimation (NPMLE) techniques to estimate both the mean and variance parameters. By accommodating varying variances among features, our proposed method leads to notable improvements in classification performance. In particular, unlike numerous prior studies that assume the distribution of heterogeneous variances follows a right‐skewed inverse gamma distribution, our proposed method demonstrates excellent performance even when the distribution of heterogeneous variances takes on left‐skewed, symmetric, or right‐skewed forms. We conducted a series of rigorous experiments to empirically validate the effectiveness of our approach. The results of these experiments demonstrate that our proposed methodology excels in accurately classifying high‐dimensional data characterized by heterogeneous variances.

Inference for Compound Exponential XLindley Model with Applications to Lifetime Data

The creating of novel models essentially stems from the requirement to appropriate describe survival cases. In this study, a novel lifetime model with two parameters is proposed and studied for modeling more types of data used in different study cases, including symmetric, asymmetric, skewed, and complex datasets. The proposed model is obtained by compounding the exponential and XLindley distributions, and it is regarded as a strong competitor for the widely applied symmetrical and non-symmetrical models. Several characteristics and statistical properties are investigated. The unknown parameters of the recommended model for the complete sample are estimated using two estimation methods; notably, maximum likelihood estimation and Bayes techniques based on several loss functions as well as an approximate tool are used to construct the confidence intervals for the unknown parameters of the suggested model. The estimation procedures are compared using a Monte Carlo simulation experiment to demonstrate their effectiveness. In the end, the applicability and flexibility of the recommended model are conducted using two real lifetime datasets. In our illustration, we compare the practicality of the recommended model with several well-known competing distributions.

Assessing the impact of non-tariff measures on Sri Lankan mango exports: insights, challenges, and recommendations

IntroductionWith the increase in non-tariff measures (NTMs) in recent years, understanding their impact on trade policies and agricultural exports is of utmost importance for countries like Sri Lanka, where the proliferation of NTMs has posed substantial impediments to its mango export industry. However, studying NTMs can be challenging due to their complex nature, diverse range, and limited information availability.MethodsThis research aims to investigate the significant effect of NTMs on Sri Lankan mango exports, identify the pivotal drivers influencing mango exports, and analyze the performance of mango exports in Sri Lanka. This study utilized a panel dataset of 16 importing countries spanning the period from 2000 to 2021. The primary focus was on examining NTM-related challenges and obstacles faced by the mango export industry in Sri Lanka. The identification and quantification of these obstacles were achieved through a multifaceted approach in which assessment of NTM-related rejections, both domestic and overseas, evaluation of NTM incidences using frequency and coverage ratio measures, and the deployment of various gravity model equations to quantify the effect of NTMs were taken into consideration. Probit, Ordinary Least Square, Random Effects, and Poisson Pseudo Maximum Likelihood estimation techniques were utilized for data analysis.ResultsThe findings indicate a significant inverse correlation between the increase in the total count of NTMs and Sri Lankan mango exports if the country aims to export more mangoes to relevant markets, while Sanitary and Phytosanitary Measures (SPS), Technical Barriers to Trade (TBT), and Pre-shipment Inspection (PSI) contributed to increased mango exports. Among other explanatory variables, the GDP of both importing and exporting countries had a positive influence on Sri Lankan mango exports. Surprisingly, the distance to the importing country had no significant effect, though it shows a negative sign.DiscussionThis study provides valuable insights into the impact of NTMs on Sri Lankan mango exports. It highlights the considerable influence of NTMs on the overall fresh fruit export sector. We recommend proactively aligning internal quality testing regulations with the standards required by destination countries to promote future expansion.

A new generalization of Samade distribution with properties and its application to lung cancer data

Abstract In this study, a new generalization of Samade distribution has been proposed. The weighted Samade distribution (WSD) is a new distribution designed for modeling real-life data. The survival function, hazard function, moments, moment-generating function, order statistics, and entropies of this distribution have all been determined. The parameters of the suggested model are estimated using the maximum likelihood estimation technique. Finally, the helpfulness and application of the distribution have been demonstrated by lung cancer data.

Generalization of Odd Ramos-Louzada generated family of distributions: Properties, characterizations, and applications to diabetes and cancer survival datasets

Probability distributions offer the best description of survival data and as a result, various lifetime models have been proposed. However, some of these survival datasets are not followed or sufficiently fitted by the existing proposed probability distributions. This paper presents a novel Kumaraswamy Odd Ramos-Louzada-G (KumORL-G) family of distributions together with its statistical features, including the quantile function, moments, probability-weighted moments, order statistics, and entropy measures. Some relevant characterizations were obtained using the hazard rate function and the ratio of two truncated moments. In light of the proposed KumORL-G family, a five-parameter sub-model, the Kumaraswamy Odd Ramos-Louzada Burr XII (KumORLBXII) distribution was introduced and its parameters were determined with the maximum likelihood estimation (MLE) technique. Monte Carlo simulation was performed and the numerical results were used to evaluate the MLE technique. The proposed probability distribution's significance and applicability were empirically demonstrated using various complete and censored datasets on the survival times of cancer and diabetes patients. The analytical results showed that the KumORLBXII distribution performed well in practice in comparison to its sub-models and several other competing distributions. The new KumORL-G for diabetes and cancer survival data is found extremely efficient and offers an enhanced and novel technique for modeling survival datasets.

A new hybrid odd exponential-Φ family: Properties and applications

The paper introduces the hybrid odd exponential-Φ (HOE-Φ) family, a novel framework for generating a continuous distribution characterized by an additional parameter. The extensive statistical properties of this family are derived and explored in detail. Parameter estimation is performed using the maximum likelihood estimation technique. The efficacy and versatility of the proposed model are demonstrated through a comparative analysis involving two distinct real-world datasets.

The Mediating Role of Career Futures between Prospective Teachers’ Career Calling and Career Adaptability

This study aims to evaluate the mediating role of career futures in the relationship between prospective teachers' career adaptability and career calling. This aim was carried out according to the quantitative research patterns relational model. The sample of this study consists of 225 prospective teachers between 18 and 39 years of age ( = 21.49, SD = 1.81). Data were collected using the Career Adapt-Abilities Scale, Career Futures Inventory, and Career Calling Scale. The two-stage Structural Equation Modeling technique tested the hypothetically determined model. Accordingly, the measurement model was first examined. Afterwards, the structural model was tested. In this model test, the Maximum Likelihood estimation technique was used. Bootstrapping analysis showed that this indirect effect was significant in 1,000 bootstrapping samples. As a result of the model test, it was determined that the career futures partially mediate the relationship between career adaptability and career calling. In line with the findings of this study, recommendations for future researchers and practitioners are presented

Development of Exponentiated Cosine Topp-Leone Generalized Family of Distributions and its Applications to Lifetime Data

The Topp-Leone distribution is widely used for modeling lifetime data across many disciplines. This paper presents the Exponentiated Cosine Topp-Leone Generalized family (ExCTLG), which is an extension of the Topp-Leone family. The research examines the mathematical properties of the ExCTLG, including the survival and hazard functions, moments, moment-generating functions, and Renyi’s entropy. Parameter estimation is carried out using the maximum likelihood estimation (MLE) techniques, and the estimated parameters consistency is validated using the Monte Carlo simulation method, thereby highlighting the superiority of MLE. The advantages and applicability of the proposed distribution are shown by analyzing two-lifetime datasets.