Statistical properties and different methods of estimation of transmuted Rayleigh distribution

Abstract

This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view, yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments, hazard rate, mean residual lifetime, mean past lifetime, mean deviation about mean and median, the stochastic ordering, various entropies, stress-strength parameter and order statistics) are derived. We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings, method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.

Generalized hyperbolic secant distribution: Properties, estimation, and applications

“…Table 4 displays the partial and overall rank of the estimators. This technique was used previously in Dey et al [12] and Tahir et al [25]. Using the results in Tables 3 and 4, we observe that the MSE values for the estimates using MM are worse (higher) than the results obtained using the other methods, while the MSE values for the estimates by ML are, in general, better (smaller) than the results obtained using the other methods.…”

A Review of Transmuted Distributions

“…The pdf appears unimodal and the hrf appears either increasing or increasing with an inflexion point. The pdf becomes increasingly unimodal with increasing positive values of k. The hrf shows presence of an inflexion point with increasing values of k. Dey et al (2017) used the TR distribution to model survival times (in days) of guinea pigs injected with different doses of tubercle bacilli (Kundu and Howlader 2010) and breaking stress (in Gba) of carbon fibers (Nadarajah et al 2013;Cordeiro et al 2014). The TR distribution was shown to provide better fits than Rayleigh, Weibull and gamma distributions.…”

A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data

“…The Weibull distribution is generated by the Swedish physicist [ 1 ]. It is commonly used for modeling reliability, electrical engineering [ 2 ], mechanical engineering [ 3 ], life time and environmental sciences data due to wide-variety of shapes. A considerable literature discussing the methods of estimation of Weibull parameters is given by [ 4 , 5 ].…”