Survival and Reliability Analysis with an Epsilon-Positive Family of Distributions with Applications

Published on May 20, 2021in Symmetry2.454
· DOI :10.3390/SYM13050908
Perla Celis1
Estimated H-index: 1
Rolando De la Cruz8
Estimated H-index: 8
+ 1 AuthorsHéctor W. Gómez19
Estimated H-index: 19
We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilon–positive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, log–normal, log–logistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilon–positive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EM–type algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.
Abstract Families of distributions on the real line have location, scale and shape parameters. Reparametrizations of such distributions, particularly involving rescalings, do not produce different families of distributions. However, from time to time, ‘extended’ or ‘generalized’ distributions are proposed that are nothing other than such reparametrizations. This note was triggered by a specific instance recently published in this journal but other examples are briefly mentioned as well.
A new two-parameter family of distribution is presented. It is derived to model the highly negatively skewed data with extreme observations. The new family of distribution is referred to as the logistic-sinh distribution, as it is derived from the logistic distribution by appropriately replacing an exponential term with a hyperbolic sine term. The resulting family provides not only negatively skewed densities with thick tails but also variety of monotonic density shapes. The space of shape param...
#1Reinaldo B. Arellano-Valle (UC: Pontifical Catholic University of Chile)H-Index: 27
#2Héctor W. Gómez (University of Atacama)H-Index: 19
Last. Fernando A. Quintana (UC: Pontifical Catholic University of Chile)H-Index: 26
view all 3 authors...
Abstract We consider a general class of asymmetric univariate distributions depending on a real-valued parameter α, which includes the entire family of univariate symmetric distributions as a special case. We discuss the connections between our proposal and other families of skew distributions that have been studied in the statistical literature. A key element in the construction of such families of distributions is that they can be stochastically represented as the product of two independent ra...
#1Rameshwar D. Gupta (UNB: University of New Brunswick)H-Index: 27
#2Debasis Kundu (IITK: Indian Institute of Technology Kanpur)H-Index: 59
Summary In this article we study some properties of a new family of distributions, namely Exponentiated Exponentialdistribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, therefore this distribution can be used as a possible alternative to a Weibull or a gamma distribu...
#1Govind S. Mudholkar (UR: University of Rochester)H-Index: 25
#2Alan D. Hutson (UF: University of Florida)H-Index: 58
Abstract A family of asymmetric distributions, which first appeared in Fechner (1897, Kollectivmasslehre. Leipzig, Engleman) is reparameterized using a skewness parameter e and named the epsilon–skew–normal family. It is denoted by ESN( θ , σ , e ). Its basic properties such as the relationship between the mean and mode, and its higher-order moments are examined. They are used to obtain simple estimators of the parameters measuring the location θ , the scale σ , and the skewness e . The maximum ...
We consider a Bayesian analysis of linear regression models that can account for skewed error distributions with fat tails.The latter two features are often observed characteristics of empirical data sets, and we will formally incorporate them in the inferential process.A general procedure for introducing skewness into symmetric distributions is first proposed.Even though this allows for a great deal of flexibility in distributional shape, tail behaviour is not affected.In addition, the impact o...
Abstract The Weibull distribution, which is frequently used for modeling survival data, is embedded in a larger family obtained by introducing an additional shape parameter. This generalized family not only contains distributions with unimodal and bathtub hazard shapes, but also allows for a broader class of monotone hazard rates. Furthermore, the distributions in this family are analytically tractable and computationally manageable. The modeling and analysis of survival data using this family i...
#1Raj S. ChhikaraH-Index: 13
#2John Leroy Folks (OSU: Oklahoma State University–Stillwater)H-Index: 5
Early occurrence of certain events such as failure or repairs is a common phenomenon in the lifetime of industrial products. Often, the log normal distribution has been found as a useful model to be applicable whenever the early occurrences dominate a lifetime distribution. In this paper we suggest the use of the inverse Gaussian distribution for a model of such lifetime behavior and discuss different reliability features of the distribution. It is shown that its failure rate is nonmonotonic, in...
#1Arthur P. Dempster (Harvard University)H-Index: 28
#2Nan M. Laird (Harvard University)H-Index: 119
Last. Donald B. Rubin (Harvard University)H-Index: 130
view all 3 authors...
The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are severa...
Cited By1
#2Zahid Khan (HU: Hazara University)H-Index: 2
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