Abstract
One of the most important applications of statistical analysis is in health research and application. Cancer studies are mostly required special statistical considerations in order to find the appropriate model for fitting the survival data. In this paper, we examine some general models leading to a weighted distribution. The developed distribution, also known as the length biased model, is referred to as the length biased Loai distribution. This distribution is a specific type of basic distribution, the Loai distribution. The length biased distribution has been compared with the original distribution. Some statistical properties of this distribution are derived, such as moments, the moment generating function, the reliability analysis, and the included functions. Also, the distribution of order statistics, quantile function, and likelihood ratio test are presented. The Bonferroni and Lorenz carvers, as well as the Rnyi and Tsallis entropies, are derived. The method of maximum likelihood estimation is used to estimate the distribution parameters. A simulation study is performed to investigate the performance of the estimation. The real data applications demonstrate that the proposed distribution can provide better results than several well-known distributions.
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