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 A New Version of the Exponentiated Exponential Distribution: Copula, Properties and Application to Relief and Survival Times

2021 ◽  
Vol 9 (2) ◽  
pp. 311-333
Author(s):  
Hanaa Elgohari
Keyword(s):  
Exponential Distribution ◽  
Hazard Function ◽  
Real Data ◽  
Likelihood Method ◽  
Type Model ◽  
Data Sets ◽  
Survival Times ◽  
Mathematical Properties ◽  
Mean Variance ◽  
New Distribution

In this paper, we introduce a new generalization of the Exponentiated Exponential distribution. Various structural mathematical properties are derived. Numerical analysis for mean, variance, skewness and kurtosis and the dispersion index is performed. The new density can be right skewed and symmetric with "unimodal" and "bimodal" shapes. The new hazard function can be "constant", "decreasing", "increasing", "increasing-constant", "upside down-constant", "decreasing nstant". Many bivariate and multivariate type model have been also derived. We assess the performance of the maximum likelihood method graphically via the biases and mean squared errors. The usefulness and flexibility of the new distribution is illustrated by means of two real data sets.

scholarly journals TRANSMUTED ARCSINE DISTRIBUTION PROPERTIES AND APPLICATION

2018 ◽  
Vol 6 (10) ◽  
pp. 38-47
Author(s):  
Salma Omar Bleed ◽  
Arwa Elsunousi Ali Abdelali
Keyword(s):  
Maximum Likelihood Method ◽  
Risk Function ◽  
Real Data ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Residual Function ◽  
Arcsine Distribution ◽  
New Distribution

The distribution of ArcSine will be developed to another new distribution using the Quadratic Rank Transmutation (QRT) method proposed by Shaw and Buckley (2007). The new distribution will be called the Transmuted ArcSine distribution, some of its mathematical characteristics such as variance, expectation, residual function, risk function, moments, moment generating function and characteristic function will be presented. The model parameters will be estimated by the maximum likelihood method. Finally, two real data sets are analyzed to illustrates the usefulness of the TAS distribution.

scholarly journals A New Generalized Weighted Weibull Distribution

2019 ◽  
pp. 161-178 ◽  
Author(s):  
Salman Abbas ◽  
Gamze Ozal ◽  
Saman Hanif Shahbaz ◽  
Muhammad Qaiser Shahbaz
Keyword(s):  
Weibull Distribution ◽  
Generating Function ◽  
Probability Generating Function ◽  
Real Data ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model

In this article, we present a new generalization of weighted Weibull distribution using Topp Leone family of distributions. We have studied some statistical properties of the proposed distribution including quantile function, moment generating function, probability generating function, raw moments, incomplete moments, probability, weighted moments, Rayeni and q th entropy. The have obtained numerical values of the various measures to see the eect of model parameters. Distribution of of order statistics for the proposed model has also been obtained. The estimation of the model parameters has been done by using maximum likelihood method. The eectiveness of proposed model is analyzed by means of a real data sets. Finally, some concluding remarks are given.

scholarly journals THE BETA EXPONENTIATED WEIBULL GEOMETRIC DISTRIBUTION: MODELING, STRUCTURAL PROPERTIES, ESTIMATION AND AN APPLICATION TO A CERVICAL INTRAEPITHELIAL NEOPLASIA DATASET

2018 ◽  
Vol 36 (4) ◽  
pp. 942
Author(s):  
Francisco LOUZADA ◽  
Ibrahim ELBATAL ◽  
Daniele Cristina Tita GRANZOTTO
Keyword(s):  
Structural Properties ◽  
Geometric Distribution ◽  
Intraepithelial Neoplasia ◽  
Random Variable ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Exponentiated Weibull ◽  
New Distribution

A new distribution, the so called beta exponentiated Weibull geometric (BEWG) distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the exponentiated Weibull geometric distribution as particular case. 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 model was showed by using a real dataset. In order to validate the results a simulation bootstrap is presented in this paper.

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.

Bounded M-O Extended Exponential Distribution with Applications

2019 ◽  
Vol 34 (1) ◽  
pp. 35-51
Author(s):  
Indranil Ghosh ◽  
Sanku Dey ◽  
Devendra Kumar
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Generating Function ◽  
Hazard Rate ◽  
Real Data ◽  
Moment Generating Function ◽  
Residual Lifetime ◽  
Model Parameters ◽  
Data Sets ◽  
Conditional Moment Generating Function

Abstract In this paper a new probability density function with bounded domain is presented. This distribution arises from the Marshall–Olkin extended exponential distribution proposed by Marshall and Olkin (1997). It depends on two parameters and can be considered as an alternative to the classical beta and Kumaraswamy distributions. It presents the advantage of not including any additional parameter(s) or special function in its formulation. The new transformed model, called the unit-Marshall–Olkin extended exponential (UMOEE) distribution which exhibits decreasing, increasing and then bathtub shaped density while the hazard rate has increasing and bathtub shaped. Various properties of the distribution (including quantiles, ordinary moments, incomplete moments, conditional moments, moment generating function, conditional moment generating function, hazard rate function, mean residual lifetime, Rényi and δ-entropies, stress-strength reliability, order statistics and distributions of sums, difference, products and ratios) are derived. The method of maximum likelihood is used to estimate the model parameters. A simulation study is carried out to examine the bias, mean squared error and 95  asymptotic confidence intervals of the maximum likelihood estimators of the parameters. Finally, the potentiality of the model is studied using two real data sets. Further, a bivariate extension based on copula concept of the proposed model are developed and some properties of the distribution are derived. The paper is motivated by two applications to real data sets and we hope that this model will be able to attract wider applicability in survival and reliability.

scholarly journals The Extended Generalized Gamma Geometric Distribution

2017 ◽  
Vol 5 (4) ◽  
pp. 48
Author(s):  
Juliano Bortolini ◽  
Marcelino A. R. Pascoa ◽  
Renato Ribeiro De Lima ◽  
Anderson C. S. Oliveira
Keyword(s):  
Geometric Distribution ◽  
Real Data ◽  
Moment Generating Function ◽  
Model Parameters ◽  
Mathematical Treatment ◽  
Data Sets ◽  
Hazard Functions ◽  
Generalized Gamma ◽  
Method Of Maximum Likelihood ◽  
New Distribution

We propose and study the so-called extended generalized gamma geometric distribution. The proposed distribution has five parameters and it can be accommodate increasing, decreasing, bathtub and unimodal shaped hazard functions. The new distribution has a large number of well-known lifetime special sub-models such as the generalized gamma geometric, Weibull geometric, gamma geometric, exponential geometric, Rayleigh geometric, half-normal geometric among others. We provide a mathematical treatment of the new distribution including explicit expressions for moments, moment generating function, mean deviations, reliability and order statistics. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. Finally, an application of the new distribution is illustrated in a real data sets.

scholarly journals Theory and Applications of the Unit Gamma/Gompertz Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1850
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rate Function ◽  
The Other ◽  
Likelihood Method ◽  
Model Parameters ◽  
Data Sets ◽  
Gompertz Distribution ◽  
Probability And Statistics ◽  
Analytical Behavior

Unit distributions are commonly used in probability and statistics to describe useful quantities with values between 0 and 1, such as proportions, probabilities, and percentages. Some unit distributions are defined in a natural analytical manner, and the others are derived through the transformation of an existing distribution defined in a greater domain. In this article, we introduce the unit gamma/Gompertz distribution, founded on the inverse-exponential scheme and the gamma/Gompertz distribution. The gamma/Gompertz distribution is known to be a very flexible three-parameter lifetime distribution, and we aim to transpose this flexibility to the unit interval. First, we check this aspect with the analytical behavior of the primary functions. It is shown that the probability density function can be increasing, decreasing, “increasing-decreasing” and “decreasing-increasing”, with pliant asymmetric properties. On the other hand, the hazard rate function has monotonically increasing, decreasing, or constant shapes. We complete the theoretical part with some propositions on stochastic ordering, moments, quantiles, and the reliability coefficient. Practically, to estimate the model parameters from unit data, the maximum likelihood method is used. We present some simulation results to evaluate this method. Two applications using real data sets, one on trade shares and the other on flood levels, demonstrate the importance of the new model when compared to other unit models.

scholarly journals A Study on A New Type 1 Half-Logistic Family of Distributions and Its Applications

2020 ◽  
Vol 8 (4) ◽  
pp. 934-949
Author(s):  
Morad Alizadeh ◽  
Alireza Nematollahi ◽  
Emrah Altun ◽  
Mahdi Rasekhi
Keyword(s):  
Residual Life ◽  
Moment Generating Function ◽  
Likelihood Method ◽  
Mean Deviation ◽  
Model Parameters ◽  
Type I ◽  
Monte Carlo Simulation Study ◽  
New Type ◽  
Application Fields ◽  
Family Of Distributions

In this paper, we propose a new class of continuous distributions with two extra shape parameters called the a new type I half logistic-G family of distributions. Some of important properties including ordinary moments, quantiles, moment generating function, mean deviation, moment of residual life, moment of reversed residual life, order statistics and extreme value are obtained. To estimate the model parameters, the maximum likelihood method is also applied by means of Monte Carlo simulation study. A new location-scale regression model based on the new type I half logistic-Weibull distribution is then introduced. Applications of the proposed family is demonstrated in many fields such as survival analysis and univariate data fitting. Empirical results show that the proposed models provide better fits than other well-known classes of distributions in many application fields.

scholarly journals Two-Parameter Nwikpe (TPAN) Distribution with Application

2021 ◽  
pp. 56-67
Author(s):  
Barinaadaa John Nwikpe ◽  
Isaac Didi Essi
Keyword(s):  
Goodness Of Fit ◽  
Continuous Distribution ◽  
Real Life ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Likelihood Method ◽  
Data Sets ◽  
Method Of Moment ◽  
Two Parameter ◽  
New Distribution

A new two-parameter continuous distribution called the Two-Parameter Nwikpe (TPAN) distribution is derived in this paper. The new distribution is a mixture of gamma and exponential distributions. A few statistical properties of the new probability distribution have been derived. The shape of its density for different values of the parameters has also been established.  The first four crude moments, the second and third moments about the mean of the new distribution were derived using the method of moment generating function. Other statistical properties derived include; the distribution of order statistics, coefficient of variation and coefficient of skewness. The parameters of the new distribution were estimated using maximum likelihood method. The flexibility of the Two-Parameter Nwikpe (TPAN) distribution was shown by fitting the distribution to three real life data sets. The goodness of fit shows that the new distribution outperforms the one parameter exponential, Shanker and Amarendra distributions for the data sets used for this study.

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