scholarly journals A Flexible Extension of Pareto Distribution: Properties and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Huda M. Alshanbari ◽  
Abd Al-Aziz Hosni El-Bagoury ◽  
Ahmed M. Gemeay ◽  
E. H. Hafez ◽  
Ahmed Sedky Eldeeb
Keyword(s):  
Residual Life ◽  
Mixture Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Global Maximum ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Data Sets ◽  
Unknown Parameters

This paper introduced a relatively new mixture distribution that results from a mixture of Fréchet–Weibull and Pareto distributions. Some properties of the new statistical model were derived, such as moments with their related measures, moment generating function, mean residual life function, and mean deviation. Furthermore , different estimation methods were introduced for determining the unknown parameters of the proposed model. Finally, we introduced three real data sets which were applied to our distribution and compared them with other well-known statistical competitive models to show the superiority of our model for fitting the three real data sets, and we can clearly see that our distribution outperforms its competitors. Also, to verify our results, we carried out the existence and uniqueness test to the log-likelihood to determine whether the roots are global maximum or not.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals Logit Truncated-Exponential Skew-Logistic Distribution with Properties and Applications

Modelling ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 776-794
Author(s):  
Liyuan Pang ◽  
Weizhong Tian ◽  
Tingting Tong ◽  
Xiangfei Chen
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Interval Data ◽  
Quantile Function ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Mean Deviation ◽  
Mean Residual Life ◽  
Unknown Parameters ◽  
Bounded Interval

In recent years, bounded distributions have attracted extensive attention. At the same time, various areas involve bounded interval data, such as proportion and ratio. In this paper, we propose a new bounded model, named logistic Truncated exponential skew logistic distribution. Some basic statistical properties of the proposed distribution are studied, including moments, mean residual life function, Renyi entropy, mean deviation, order statistics, exponential family, and quantile function. The maximum likelihood method is used to estimate the unknown parameters of the proposed distribution. More importantly, the applications to three real data sets mainly from the field of engineering science prove that the logistic Truncated exponential skew logistic distribution fits better than other bounded distributions.

scholarly journals Kumaraswamy Distribution Based on Alpha Power Transformation Methods

2021 ◽  
pp. 14-29
Author(s):  
H. E. Hozaien ◽  
G. R. AL Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Residual Life ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Mean Residual Life ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Kumaraswamy Distribution

In this paper, the alpha power Kumaraswamy distribution, new alpha power transformed Kumaraswamy distribution and new extended alpha power transformed Kumaraswamy distribution are presented. Some statistical properties of the three distributions are derived including quantile function, moments and moment generating function, mean residual life and order statistics. Estimation of the unknown parameters based on maximum likelihood estimation are obtained. A simulation study is carried out. Finally, a real data set is applied.

scholarly journals On Erlang-Truncated Exponential Distribution: Theory and Application

2021 ◽  
pp. 155-168
Author(s):  
Ibrahim Elbatal ◽  
A. Aldukeel
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Data Sets ◽  
Survival Times ◽  
New Distribution ◽  
Better Than

In this article, we introduce a new distribution called the McDonald Erlangtruncated exponential distribution. Various structural properties including explicit expressions for the moments, moment generating function, mean deviation of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated by two real data sets. The new model is much better than other important competitive models in modeling relief times and survival times data sets.

scholarly journals The Beta Exponential Fréchet Distribution with Applications

2017 ◽  
Vol 46 (1) ◽  
pp. 41-63 ◽  
Author(s):  
M.E. Mead ◽  
Ahmed Z. Afify ◽  
G.G. Hamedani ◽  
Indranil Ghosh
Keyword(s):  
Residual Life ◽  
Real Data ◽  
Mean Residual Life ◽  
Model Parameters ◽  
Data Sets ◽  
Nested Models ◽  
Fréchet Distribution ◽  
Proposed Model ◽  
Mean Inactivity Time ◽  
Frechet Distribution

We define and study a new generalization of the Fréchet distribution called the beta exponential Fréchet distribution. The new model includes thirty two special models. Some of its mathematical properties, including explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean residual life, mean inactivity time, order statistics and entropies are derived. The method of maximum likelihood is proposed to estimate the model parameters. A small simulation study is alsoreported. Two real data sets are applied to illustrate the flexibility of the proposed model compared with some nested and non-nested models.

scholarly journals Binomial-exponential 2 Distribution: Different Estimation Methods and Weather Applications

2017 ◽  
Vol 18 (2) ◽  
pp. 0233 ◽  
Author(s):  
Hassan S Bakouch ◽  
Sanku Dey ◽  
Pedro Luiz Ramos ◽  
Francisco Louzada
Keyword(s):  
Method Of Moments ◽  
Minimum Distance ◽  
Real Data ◽  
Ordinary Least Squares ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Anderson Darling ◽  
Von Mises ◽  
Modified Moments

In this paper, we have considered different estimation methods of the unknown parameters of a binomial-exponential 2 distribution. First, we briefly describe different frequentist approaches such as the method of moments, modified moments, ordinary least-squares estimation, weightedleast-squares estimation, percentile, maximum product of spacings, Cramer-von Mises type minimum distance, Anderson-Darling and Right-tail Anderson-Darling, and compare them using extensive numerical simulations. We apply our proposed methodology to three real data sets related to the total monthly rainfall during April, May and September at Sao Carlos, Brazil.

scholarly journals Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 985 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
Mohammed Elgarhy
Keyword(s):  
Statistical Treatment ◽  
Continuous Distribution ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Strength Parameter ◽  
Data Sets ◽  
Type I ◽  
Unknown Parameters ◽  
Power Series Expansions

In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp–Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.

scholarly journals The Topp-Leone Generalized Inverted Exponential Distribution with Real Data Applications

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1144
Author(s):  
Zakeia A. Al-Saiary ◽  
Rana A. Bakoban
Keyword(s):  
Maximum Likelihood ◽  
Survival Function ◽  
Information Matrix ◽  
Real Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Deviation ◽  
Data Sets ◽  
Unknown Parameters ◽  
Illustrative Purpose

In this article, a new three parameters lifetime model called the Topp-Leone Generalized Inverted Exponential (TLGIE) Distribution is introduced. Various properties of the model are derived, including moments, quantile function, survival function, hazard rate function, mean deviation and mode. The method of maximum likelihood is used to estimate the unknown parameters. The properties of the maximum likelihood estimators using Fisher information matrix are studied. Three real data sets are applied for illustrative purpose of this study.

scholarly journals Inverse Power Akash Probability Distribution with Applications

2020 ◽  
pp. 1-32
Author(s):  
Samuel U. Enogwe ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Inverse Power ◽  
Data Sets ◽  
Unknown Parameters ◽  
Bathtub Shape ◽  
Heavy Tailed

This paper introduces an inverse power Akash distribution as a generalization of the Akash distribution to provide better fits than the Akash distribution and some of its known extensions. The fundamental properties of the proposed distribution such as the shapes of the distribution, moments, mean, variance, coefficient of variation, skewness, kurtosis, moment generating function, quantile function, Rényi entropy, stochastic ordering and the distribution of order statistics have been derived. The proposed distribution is observed to be a heavy-tailed distribution and can also be used to model data with upside-down bathtub shape for its hazard rate function. The maximum likelihood estimators of the unknown parameters of the proposed distribution have been obtained. Two numerical examples are given to demonstrate the applicability of the proposed distribution and for the two real data sets, the proposed distribution is found to be superior in its ability to sufficiently model heavy-tailed data than Akash, inverse Akash and power Akash distributions respectively.

scholarly journals On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

2021 ◽  
Vol 2 ◽  
pp. 2
Author(s):  
Femi Samuel Adeyinka
Keyword(s):  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Data Sets ◽  
Hazard Functions ◽  
Lorenz Curves ◽  
Conditional Moments ◽  
New Family ◽  
Family Of Distributions

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed.  The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

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