Abstract
A more flexible two-parameter model named the Topp Leone inverse Lindley model is investigated. Some basic mathematical properties such as quantile, moments, order statistics, and Rényi entropy of the new distribution are considered. Plot analysis for mean, variance, skewness, and kurtosis is performed. The density of the new model can be right skewed and decreasing with unimodal and bimodal shapes. Also, its hazard rate function can be decreasing and upside-down. The maximum likelihood (ML) estimation method is used to estimate the parameters of the distribution. The simulation study is executed to investigate the effectiveness of the estimates. The potential of the distribution is demonstrated through the application of the real biomedical dataset.
Highlights
Introduction e ToppLeone (TL-G) class of distributions was introduced by Al-Shomrani et al [1]
Suppose X1 < X2 < . . . < Xn is an order sample from Topp Leone inverse Lindley (TLIL) population, the pdf of the ith ordered statistics is given as f xi: n
(i) 5000 random samples of size n 50, 100, and 200 are generated from TLIL distribution (ii) Exact values of parameters are choiced (iii) e maximum likelihood (ML) estimates, Mean square errors (MSEs), biases, lower bound (LB), upper bound (UB), and average length (AL) for selected values of parameters are calculated (iv) Numerical outcomes are given in Tables 1–5 based on complete
Summary
Suppose a random variable X follows the TLIL model, the reliability function R(x), hazard rate function (hrf ) h(x), inverse hazard rate function τ(x), and cumulative hazard rate function H(x) for the TLIL distribution are given by.
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