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. 2020 May 26:2020:4650520.
doi: 10.1155/2020/4650520. eCollection 2020.

A New Extended- X Family of Distributions: Properties and Applications

Mi Zichuan  1 , Saddam Hussain  1 , Anum Iftikhar  1 , Muhammad Ilyas  2 , Zubair Ahmad  3 , Dost Muhammad Khan  4 , Sadaf Manzoor  5
Affiliations

A New Extended- X Family of Distributions: Properties and Applications

Mi Zichuan et al. Comput Math Methods Med. .

Abstract

During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-t, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.

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Conflict of interest statement

There is no competing interest regarding the publication of this paper.

Figures

Figure 1
Figure 1
Some possible shapes of the density function of the NE-W distribution.
Figure 2
Figure 2
Some possible shapes for the hazard function of the NE-W distribution.
Figure 3
Figure 3
Plots of the estimated parameters and MSEs for α = 0.9, θ = 1.2, and γ = 0.7.
Figure 4
Figure 4
Plots of the biases and absolute biases for α = 0.9, θ = 1.2, and γ = 0.7.
Figure 5
Figure 5
Plots of the estimated parameters and MSEs for α = 1.5, θ = 0.4, and γ = 0.7.
Figure 6
Figure 6
Plots of the biases and absolute biases for α = 1.5, θ = 0.4, and γ = 0.7.
Figure 7
Figure 7
Estimated cdf and Kaplan Meier Survival plots of the NE-W distribution for data 1.
Figure 8
Figure 8
PP plot of the NE-W distribution and the box plot for data 1.
Figure 9
Figure 9
Estimated cdf and Kaplan Meier survival plots of the NE-W distribution for data 2.
Figure 10
Figure 10
PP plot of the NE-W distribution and the box plot for data 2.
Figure 11
Figure 11
Estimated cdf and Kaplan Meier survival plots of the NE-W distribution for data 3.
Figure 12
Figure 12
PP plot of the NE-W distribution and the Box plot for data 3.
See this image and copyright information in PMC

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