Abstract
We study in this manuscript a new one-parameter model called sine inverse Rayleigh (SIR) model that is a new extension of the classical inverse Rayleigh model. The sine inverse Rayleigh model is aiming to provide more fitting for real data sets of purposes. The proposed extension is more flexible than the original inverse Rayleigh (IR) model and it hasmany applications in physics and medicine. The sine inverse Rayleigh distribution can havea uni-model and right skewed probability density function (PDF). The hazard rate function (HRF) of sine inverse Rayleigh distribution can be increasing and J-shaped. Several of thenew model’s fundamental characteristics, namely quantile function, moments, incompletemoments, Lorenz and Bonferroni Curves are studied. Four classical estimation methods forthe population parameters, namely least squares (LS), weighted least squares (WLS), maximum likelihood (ML), and percentile (PC) methods are discussed, and the performanceof the four estimators (namely LS, WLS, ML and PC estimators) are also compared bynumerical implementations. Finally, three sets of real data are utilized to compare the behavior of the four employed methods for finding an optimal estimation of the new distribution.
Highlights
Reference [1] investigated a significant distribution in analysis of lifetime, namely the inverse Rayleigh (IR) model
We study in this manuscript a new one-parameter model called sine inverse Rayleigh (SIR) model that is a new extension of the classical inverse Rayleigh model
We estimate the model parameters according to the maximum likelihood (ML), least squares (LS), weighted least squares (WLS) and PC methods
Summary
Reference [1] investigated a significant distribution in analysis of lifetime, namely the inverse Rayleigh (IR) model. The IR model’s considered probability density function (PDF) and the corresponding distribution function (CDF) are given by gðyÞ 1⁄4 2hyÀ3eÀyh ; h . Many different statisticians are attracted by generated families of distributions as: sine generated (S-G) by [10], Type II half logistic-G by [11], odd Frèchet-G by [12], truncated Cauchy power-G by [13], transmuted odd Fréchet-G by [14], exponentiated M-G by [15], Topp-Leone odd Fréchet-G studied in [16], among others. We put forward a novel lifetime model with one parameter named sine inverse Rayleigh (SIR). 1 and 2 present the PDF and HRF plots of the SIR distribution, respectively, for various θ values. 1 and 2 exhibit that the SIR distribution can have a uni-model and right skewed PDF, while its HRF can be J-shaped and increasing
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