Unit upper truncated Weibull distribution with extension to 0 and 1 inflated model – Theory and applications

Okorie, Idika E.; Afuecheta, Emmanuel; Bakouch, Hassan S.

doi:10.1016/j.heliyon.2023.e22260

Cited by 5 publications

(2 citation statements)

References 37 publications

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“…This range encompasses well-established models, such as the beta and Kumaraswamy distributions. Additionally, the literature presents various unitary distribution models, including the Topp-Leone distribution [2]: unit-gamma [3], log-Lindley [4], twoparameter unit-logistic [5], two-parameter unit-Birnbaum-Saunders [6], unit-Weibull [7], unit-Gompertz [8], unit-inverse Gaussian [9], unit modified Burr-III [10], one-parameter unit-Lindley [11], alpha-unit [12], modified unit-half-normal [13], unit-half-normal [14], unit-exponential [15] and unit upper truncated Weibull [16].…”

Section: Introductionmentioning

confidence: 99%

Statistical Advancement of a Flexible Unitary Distribution and Its Applications

Salinas,

Bakouch,

Almuhayfith

et al. 2024

Axioms

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A flexible distribution has been introduced to handle random variables in the unit interval. This distribution is based on an exponential transformation of the truncated positive normal distribution with two parameters and can effectively fit data with varying degrees of skewness and kurtosis. Therefore, it presents an alternative for modeling this type of data. Several mathematical and statistical properties of this distribution have been derived, such as moments, hazard function, the Bonferroni curve, and entropy. Moreover, we investigate the characterizations of the proposed distribution based on its hazard function. Parameter estimation has been performed using both the maximum likelihood method and method of the moments. Because of this, we were able to determine the best critical region and the information matrix, facilitating the calculation of asymptotic confidence intervals. A simulation study is presented to analyze the behavior of the obtained estimators for different sample sizes. To demonstrate the suitability of the proposed distribution, applications and goodness-of-fit tests have been performed on two practical data sets.

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Section: Introductionmentioning

confidence: 99%

Statistical Advancement of a Flexible Unitary Distribution and Its Applications

Salinas,

Bakouch,

Almuhayfith

et al. 2024

Axioms

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“…The benefit of these unit distributions lies in their ability to enhance the flexibility of the original distribution across the unit interval without introducing additional parameters. For this purpose, many proposed unit distributions, such as unit gamma [3], log-xgamma [4], unit inverse Gaussian [5], unit Gompertz [6], unit Birnbaum-Saunders [7], unit half-normal [8], unit exponential probability [9], and unit upper truncated Weibull [10], have been proposed recently in the literature. In these studies, the performance of the unit distributions is examined based on parameter estimation and practical data applications.…”

Section: Introductionmentioning

confidence: 99%

On the Maximum Likelihood Estimators’ Uniqueness and Existence for Two Unitary Distributions: Analytically and Graphically, with Application

Alomair,

Akdoğan,

Bakouch

et al. 2024

Symmetry

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Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.

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