Type II Power Topp-Leone Generated Family of Distributions with Statistical Inference and Applications
TL;DR: This paper presents and study a new family of continuous distributions, called the type II power Topp-Leone-G family, which provides a natural extension of the so-called type II Topp, Leone, G family, thanks to the use of an additional shape parameter, and shows that it outperforms other well-known models defined with the same baseline distribution.
Abstract: In this paper, we present and study a new family of continuous distributions, called the type II power Topp-Leone-G family. It provides a natural extension of the so-called type II Topp-Leone-G family, thanks to the use of an additional shape parameter. We determine the main properties of the new family, showing how they depend on the involving parameters. The following points are investigated: shapes and asymptotes of some important functions, quantile function, some mixture representations, moments and derivations, stochastic ordering, reliability and order statistics. Then, a special model of the family based on the inverse exponential distribution is introduced. It is of particular interest because the related probability functions are tractable and possess various kinds of asymmetric shapes. Specially, reverse J, left skewed, near symmetrical and right skewed shapes are observed for the corresponding probability density function. The estimation of the model parameters is performed by the use of three different methods. A complete simulation study is proposed to illustrate their numerical efficiency. The considered model is also applied to analyze two different kinds of data sets. We show that it outperforms other well-known models defined with the same baseline distribution, proving its high level of adaptability in the context of data analysis.
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TL;DR: A generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter, which constitutes a new four-parameter lifetime distribution which brightens by the multitude of different shapes of the corresponding probability density and hazard rate functions.
Abstract: In this paper, we propose a generalization of the so-called truncated inverse Weibull-generated family of distributions by the use of the power transform, adding a new shape parameter. We motivate this generalization by presenting theoretical and practical gains, both consequences of new flexible symmetric/asymmetric properties in a wide sense. Our main mathematical results are about stochastic ordering, uni/multimodality analysis, series expansions of crucial probability functions, probability weighted moments, raw and central moments, order statistics, and the maximum likelihood method. The special member of the family defined with the inverse Weibull distribution as baseline is highlighted. It constitutes a new four-parameter lifetime distribution which brightensby the multitude of different shapes of the corresponding probability density and hazard rate functions. Then, we use it for modelling purposes. In particular, a complete numerical study is performed, showing the efficiency of the corresponding maximum likelihood estimates by simulation work, and fitting three practical data sets, with fair comparison to six notable models of the literature.
23 citations
TL;DR: This article proposes an extension of the odd Frechet family through the so-called “Topp-Leone strategy”, aiming to improve its overall flexibility by adding a shape parameter to offer original distributions with modifiable properties, from which adaptive and pliant statistical models can be derived.
Abstract: Recent studies have pointed out the potential of the odd Frechet family (or class) of continuous distributions in fitting data of all kinds In this article, we propose an extension of this family through the so-called “Topp-Leone strategy”, aiming to improve its overall flexibility by adding a shape parameter The main objective is to offer original distributions with modifiable properties, from which adaptive and pliant statistical models can be derived For the new family, these aspects are illustrated by the means of comprehensive mathematical and numerical results In particular, we emphasize a special distribution with three parameters based on the exponential distribution The related model is shown to be skillful to the fitting of various lifetime data, more or less heterogeneous Among all the possible applications, we consider two data sets of current interest, linked to the COVID-19 pandemic They concern daily cases confirmed and recovered in Pakistan from March 24 to April 28, 2020 As a result of our analyzes, the proposed model has the best fitting results in comparison to serious challengers, including the former odd Frechet model © 2020 Tech Science Press All rights reserved
22 citations
TL;DR: The truncated Burr X generated family as discussed by the authors is a family of univariate continuous-type distributions, which can be expressed analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions.
Abstract: In this article, the "truncated-composed" scheme was applied to the Burr X distribution to motivate a new family of univariate continuous-type distributions, called the truncated Burr X generated family. It is mathematically simple and provides more modeling freedom for any parental distribution. Additional functionality is conferred on the probability density and hazard rate functions, improving their peak, asymmetry, tail, and flatness levels. These characteristics are represented analytically and graphically with three special distributions of the family derived from the exponential, Rayleigh, and Lindley distributions. Subsequently, we conducted asymptotic, first-order stochastic dominance, series expansion, Tsallis entropy, and moment studies. Useful risk measures were also investigated. The remainder of the study was devoted to the statistical use of the associated models. In particular, we developed an adapted maximum likelihood methodology aiming to efficiently estimate the model parameters. The special distribution extending the exponential distribution was applied as a statistical model to fit two sets of actuarial and financial data. It performed better than a wide variety of selected competing non-nested models. Numerical applications for risk measures are also given.
11 citations
TL;DR: This work discusses new theoretical facts and introduces a natural extension of the Muth generated class of distributions via the transmuted scheme, showing that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry.
Abstract: Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model.
10 citations
References
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TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.
Abstract: The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative distribution function and $\psi(t)$ is some nonnegative weight function $(0 \leqq t \leqq 1)$, we consider $n^{\frac{1}{2}} \sup_{-\infty
3,082 citations
"Type II Power Topp-Leone Generated ..." refers methods in this paper
...Right-Tail Anderson-Darling Method of Estimation We now discuss the right-tail Anderson-Darling estimates (RTADEs) of α, β and θ pioneered by [30]....
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Book•
01 Jan 1994
TL;DR: General Theory.
Abstract: General Theory. Applications in Statistics. Applications in Biology. Applications in Economics. Applications in Operations Research. Applications in Reliability Theory.
2,242 citations
"Type II Power Topp-Leone Generated ..." refers background in this paper
...For the complete theory, we refer the reader to [26]....
[...]
TL;DR: In this paper, a reliability and maintainability study of computer control (CNC) machine tools is described, where the lognormal and Weibull distribution are used to describe time between failures and the repair times.
215 citations
"Type II Power Topp-Leone Generated ..." refers methods in this paper
...In order to motivate this choice of baseline, let us recall that the inverse exponential distribution was introduced by [24] as a suitable alternative to the standard exponential distribution....
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TL;DR: A family of J-Shaped Frequency Functions (JFFs) as mentioned in this paper is a family of j-shaved frequency functions, which is related to our JFFs.
Abstract: (1955). A Family of J-Shaped Frequency Functions. Journal of the American Statistical Association: Vol. 50, No. 269, pp. 209-219.
184 citations
"Type II Power Topp-Leone Generated ..." refers background in this paper
...Introduction Among the existing distributions with support over the unit interval, the so-called Topp-Leone distribution, introduced by [1], is one of the most useful....
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178 citations
"Type II Power Topp-Leone Generated ..." refers background in this paper
...The first data set contains the ball bearing data, which indicates the number of revolutions before failure for ball bearing (see [37])....
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