Abstract
Lifetime distributions are an important statistical tools to model the different characteristics of lifetime data sets. The statistical literature contains very sophisticated distributions to analyze these kind of data sets. However, these distributions have many parameters which cause a problem in estimation step. To open a new opportunity in modeling these kind of data sets, we propose a new extension of half-logistic distribution by using the odd Lindley-G family of distributions. The proposed distribution has only one parameter and simple mathematical forms. The statistical properties of the proposed distributions, including complete and incomplete moments, quantile function and Rényi entropy, are studied in detail. The unknown model parameter is estimated by using the different estimation methods, namely, maximum likelihood, least square, weighted least square and Cramer-von Mises. The extensive simulation study is given to compare the finite sample performance of parameter estimation methods based on the complete and progressive Type-II censored samples. Additionally, a new log-location-scale regression model is introduced based on a new distribution. The residual analysis of a new regression model is given comprehensively. To convince the readers in favour of the proposed distribution, three real data sets are analyzed and compared with competitive models. Empirical findings show that the proposed one-parameter lifetime distribution produces better results than the other extensions of half-logistic distribution.
Highlights
There are many distributions in the statistics literature
The test statistics value of Kolmogorov-Smirnov test (KS) tests of the least-square estimation (LSE), weighted LSE (WLSE), and Cramer-von Mises estimation (CVME) methods are smaller than those of the maximum likelihood estimation (MLE) method for the OLiHL distribution. This result shows the fact that LSE, WLSE, and CVME methods could be more appropriate estimation methods than MLE for this data set
This study proposes a new one-parameter lifetime distribution, called as odd Lindley halflogistic distribution, shortly OLiHL distribution
Summary
There are many distributions in the statistics literature. each data sings its song. To increase the accuracy in data modeling, the researchers have introduced flexible distributions for both discrete and continuous cases. The generalization of the exponential, Weibull, generalized half-normal and Lindley distributions have gained attention by researchers because of their importance in lifetime and reliability modeling. Apart from these distributions, the Half-logistic (HL) is an important distribution for reliability analysis and increased its popularity in recent years. The probability density function (pdf) of the HL distribution is
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