Some New Facts about the Unit-Rayleigh Distribution with Applications

By Rashad A. R. Bantan, Christophe Chesneau, Farrukh Jamal, Mohammed Elgarhy, Muhammad Hussain Tahir, Aqib Ali, Muhammad Zubair, Sania Anam. Mathematics, 2020

73 citations recorded by the source corpus.

The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precisely, on the theoretical level, we contribute to the following aspects: (i) we bring new characteristics on the form analysis of its main probabilistic and reliability functions, and show that the possible mode has a simple analytical expression, (ii) we prove new stochastic ordering results, (iii) we expose closed-form expressions of the incomplete and probability weighted moments at the basis of various probability functions and measures, (iv) we investigate distributional properties of the order statistics, (v) we show that the reliability coefficient can have a simple ratio expression, (vi) we provide a tractable expansion for the Tsallis entropy and (vii) we propose some bivariate unit-Rayleigh distributions. On a practical level, we show that the maximum likelihood estimate has a quite simple closed-form. Three data sets are analyzed and adjusted, revealing that the unit-Rayleigh distribution can be a better alternative to standard one-parameter unit distributions, such as the one-parameter Kumaraswamy, Topp–Leone, one-parameter beta, power and transmuted distributions.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f04ba230f07664c8ca24589727381da78f6ccce0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Mohammed Elgarhy
2. Christophe Chesneau

In Statistics and Probability

1. Farrukh Jamal
2. Christophe Chesneau
3. Mohammed Elgarhy
4. Rashad A. R. Bantan

Citations in the corpus

• Theory and Applications of the Unit Gamma/Gompertz Distribution (2021, methodology): “In this regard, we compare the fit of the proposed UG/G model and those of the Kumaraswamy (Kw), beta (Beta), UR (recalling that it refers to the unit Rayleigh distribution by [10]), Topp-Leone (Topp), power (Power), and Transmuted (TM) models.”