scholarly journals A family of Gamma-generated distributions: Statistical properties and applications

2021 ◽  
pp. 096228022110092
Author(s):  
Hormatollah Pourreza ◽  
Ezzatallah Baloui Jamkhaneh ◽  
Einolah Deiri
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Monte Carlo Simulation Study ◽  
Hazard Functions ◽  
Distribution Probability ◽  
Method Of Maximum Likelihood ◽  
Special Case

In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets. Mathematics Subject Classification: 62E99; 62E15

scholarly journals The Iwok-Nwikpe Distribution: Statistical Properties and Its Application

2021 ◽  
pp. 35-45
Author(s):  
Iwok Iberedem Aniefiok ◽  
Barinaadaa John Nwikpe
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Survival Function ◽  
Medical Science ◽  
Mathematical Expression ◽  
Real Data ◽  
Moment Generating Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Data Sets

In this paper, a new continuous probability distribution named Iwok-Nwikpe distribution is proposed. Some essential statistical properties of the proposed probability distribution have been derived. The graphs of the survival function, probability density function (p.d.f) and cumulative distribution function (c.d.f) were plotted at different values of the parameter. The mathematical expression for the moment generating function (mgf) was derived. Consequently, the first three crude moments were obtained; the distribution of order statistics, the second and third moments corrected for the mean have also been derived. The parameter of the Iwok-Nwikpe distribution was estimated by means of maximum likelihood technique. To establish the goodness of fit of the Iwok-Nwikpe distribution, three real data sets from engineering and medical science were fitted to the distribution. Findings of the study revealed that the Iwok-Nwikpe distribution performed better than the one parameter exponential distribution and other competing models used for the study.

scholarly journals The Generalized Gamma – Exponentiated Weibull Distribution with its Properties

2020 ◽  
Vol 31 (2) ◽  
pp. 30
Author(s):  
Salah Hamza Abid ◽  
Nadia Hashim Al-Noor ◽  
Mohammad Abd Alhussein Boshi
Keyword(s):  
Weibull Distribution ◽  
Simulated Data ◽  
Quantile Function ◽  
Cumulative Distribution ◽  
Generalized Gamma ◽  
Distribution Probability ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Rate Functions ◽  
Special Case

In this paper, we present the Generalized Gamma-Exponentiated Weibull distribution as a special case of new generated Generalized Gamma - G family of probability distribution. The cumulative distribution, probability density, reliability and hazard rate functions are introduced. Furthermore, the most vital statistical properties, for instance, the r-th moment, characteristic function, quantile function, simulated data, Shannon and relative entropies besides the stress-strength model are obtained.

scholarly journals The Exponentiated Kumaraswamy-Weibull Distribution with Application to Real Data

2017 ◽  
Vol 6 (6) ◽  
pp. 167 ◽  
Author(s):  
Fathy Helmy Eissa
Keyword(s):  
Weibull Distribution ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Excellent Performance ◽  
Hazard Functions ◽  
Positive Data ◽  
Special Cases ◽  
Exponentiated Weibull

A new five-parameter lifetime distribution called the exponentiated Kumaraswamy-Weibull distribution is introduced. It includes several important sub-models as special cases such as exponentiated Weibull, Kumaraswamy-Weibull, exponentiated exponential, exponentiated Rayleigh and Weibull. Essential mathematical and statistical properties for the distribution are presented. A proximate form of the mode is derived and it can be used to derive mode forms of other well-known distributions. Important parametric characterizations for probability density and hazard functions are discussed. The estimation of the parameters by maximum likelihood method is discussed. Three real data sets are used to show its excellent performance fit over existing popular lifetime models. It is effective model to analyze several positive data sets.

scholarly journals Bivariate exponentiated discrete Weibull distribution: statistical properties, estimation, simulation and applications

2019 ◽  
Vol 14 (1) ◽  
pp. 29-42 ◽  
Author(s):  
M. El- Morshedy ◽  
M. S. Eliwa ◽  
A. El-Gohary ◽  
A. A. Khalil
Keyword(s):  
Weibull Distribution ◽  
Joint Probability ◽  
Discrete Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Statistical Properties ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Model Parameters ◽  
Probability Mass Function

AbstractIn this paper, a new bivariate discrete distribution is defined and studied in-detail, in the so-called the bivariate exponentiated discrete Weibull distribution. Several of its statistical properties including the joint cumulative distribution function, joint probability mass function, joint hazard rate function, joint moment generating function, mathematical expectation and reliability function for stress–strength model are derived. Its marginals are exponentiated discrete Weibull distributions. Hence, these marginals can be used to analyze the hazard rates in the discrete cases. The model parameters are estimated using the maximum likelihood method. Simulation study is performed to discuss the bias and mean square error of the estimators. Finally, two real data sets are analyzed to illustrate the flexibility of the proposed model.

scholarly journals THE POWER MUTH DISTRIBUTION∗

2017 ◽  
Vol 22 (2) ◽  
pp. 186-201 ◽  
Author(s):  
Pedro Jodra ◽  
Hector Wladimir Gomez ◽  
Maria Dolores Jimenez-Gamero ◽  
Maria Virtudes Alba-Fernandez
Keyword(s):  
Probability Distributions ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Failure Rate Function ◽  
Monte Carlo Simulation Study ◽  
New Model ◽  
Practical Usefulness ◽  
Method Of Maximum Likelihood

Muth introduced a probability distribution with application in reliability theory. We propose a new model from the Muth law. This paper studies its statistical properties, such as the computation of the moments, computer generation of pseudo-random data and the behavior of the failure rate function, among others. The estimation of parameters is carried out by the method of maximum likelihood and a Monte Carlo simulation study assesses the performance of this method. The practical usefulness of the new model is illustrated by means of two real data sets, showing that it may provide a better fit than other probability distributions.

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 Generalized Beta-Exponential Weibull Distribution and its Applications

2020 ◽  
Vol 24 (1) ◽  
pp. 1-33
Author(s):  
N. I. Badmus ◽  
◽  
Olanrewaju Faweya ◽  
K. A. Adeleke ◽  
◽  
...  
Keyword(s):  
Weibull Distribution ◽  
Information Matrix ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Model Parameters ◽  
Data Sets ◽  
Hazard Functions ◽  
Generalized Distributions

In this article, we investigate a distribution called the generalized beta-exponential Weibull distribution. Beta exponential x family of link function which is generated from family of generalized distributions is used in generating the new distribution. Its density and hazard functions have different shapes and contains special case of distributions that have been proposed in literature such as beta-Weibull, beta exponential, exponentiated-Weibull and exponentiated-exponential distribution. Various properties of the distribution were obtained namely; moments, generating function, Renyi entropy and quantile function. Estimation of model parameters through maximum likelihood estimation method and observed information matrix are derived. Thereafter, the proposed distribution is illustrated with applications to two different real data sets. Lastly, the distribution clearly shown that is better fitted to the two data sets than other distributions.

scholarly journals The Flexible Burr X-G Family: Properties, Inference, and Applications in Engineering Science

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 474
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Hazem Al-Mofleh ◽  
Ahmed M. Gemeay ◽  
Ahmed Z. Afify ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Exponential Model ◽  
Statistical Properties ◽  
Engineering Science ◽  
Data Sets ◽  
Engineering Sciences ◽  
General Statistical ◽  
Anderson Darling

In this paper, we introduce a new flexible generator of continuous distributions called the transmuted Burr X-G (TBX-G) family to extend and increase the flexibility of the Burr X generator. The general statistical properties of the TBX-G family are calculated. One special sub-model, TBX-exponential distribution, is studied in detail. We discuss eight estimation approaches to estimating the TBX-exponential parameters, and numerical simulations are conducted to compare the suggested approaches based on partial and overall ranks. Based on our study, the Anderson–Darling estimators are recommended to estimate the TBX-exponential parameters. Using two skewed real data sets from the engineering sciences, we illustrate the importance and flexibility of the TBX-exponential model compared with other existing competing distributions.

scholarly journals On a new distribution based on the arccosine function

2021 ◽  
Author(s):  
Christophe Chesneau ◽  
Lishamol Tomy ◽  
Jiju Gillariose
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Hazard Rate ◽  
Survival Function ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Power Functions ◽  
New Distribution

AbstractThis note focuses on a new one-parameter unit probability distribution centered around the inverse cosine and power functions. A special case of this distribution has the exact inverse cosine function as a probability density function. To our knowledge, despite obvious mathematical interest, such a probability density function has never been considered in Probability and Statistics. Here, we fill this gap by pointing out the main properties of the proposed distribution, from both the theoretical and practical aspects. Specifically, we provide the analytical form expressions for its cumulative distribution function, survival function, hazard rate function, raw moments and incomplete moments. The asymptotes and shape properties of the probability density and hazard rate functions are described, as well as the skewness and kurtosis properties, revealing the flexible nature of the new distribution. In particular, it appears to be “round mesokurtic” and “left skewed”. With these features in mind, special attention is given to find empirical applications of the new distribution to real data sets. Accordingly, the proposed distribution is compared with the well-known power distribution by means of two real data sets.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

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