The odd Fréchet inverse Rayleigh distribution: statistical properties and applications

Abstract

We propose a new distribution with two parameters called the odd Fréchet inverse Rayleigh (OFIR) distribution. The new model can be more flexible. Several of its statistical properties are studied. The maximum likelihood (ML) estimation is used to drive estimators of OFIR parameters. The importance and flexibility of the new model is assessed using one real data set.

Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

“…The estimation of the Rényi entropy and q-entropy is also discussed by using the plugging and ML methods. Then, we show that the fits provided by the HLIR model can accommodate data with various features, and can demonstrate better goodness-of-fits than the three following extended IR two-parameter models: the TIITLIR model (by [21]), TIR model (by [14]) and OFIR model (by [20]), and than the former one-parameter IR model as well. Two practical data sets are analyzed in this regard.…”

“…Also, among the amount of works investigating the statistical aspects of the IR distribution, the reader can be referred to [4][5][6][7][8][9][10][11][12].In the recent years, several extensions of the IR distribution were developed, using different mathematical techniques, often at the basis of general families of distributions. Among them, there are the beta IR (BIR) distribution by [13], transmuted IR (TIR) distribution by [14], modified IR (MIR) distribution by [15], transmuted modified IR (TMIR) distribution by [16], transmuted exponentiated IR (TEIR) distribution by [17], Kumaraswamy exponentiated IR (KEIR) distribution by [18], weighted IR (WIR) distribution by [19], odd Fréchet IR (OFIR) distribution by [20], type II Topp-Leone IR (TIITLIR) distribution by [21], type II Topp-Leone generalized IR (TIITLGIR) distribution by [22] and exponentiated IR (EIR) distribution by [23].However, to the best of our knowledge, the use of the half-logistic transformation to extend the IR distribution remains unexplored, despite recent success in this regard. This half-logistic transformation was pioneered by [24] in the context of the half logistic generated (HL-G) family of continuous distributions.…”

“…In the recent years, several extensions of the IR distribution were developed, using different mathematical techniques, often at the basis of general families of distributions. Among them, there are the beta IR (BIR) distribution by [13], transmuted IR (TIR) distribution by [14], modified IR (MIR) distribution by [15], transmuted modified IR (TMIR) distribution by [16], transmuted exponentiated IR (TEIR) distribution by [17], Kumaraswamy exponentiated IR (KEIR) distribution by [18], weighted IR (WIR) distribution by [19], odd Fréchet IR (OFIR) distribution by [20], type II Topp-Leone IR (TIITLIR) distribution by [21], type II Topp-Leone generalized IR (TIITLGIR) distribution by [22] and exponentiated IR (EIR) distribution by [23].…”

A New Three-Parameter Weibull Inverse Rayleigh Distribution: Theoretical Development and Applications

“…The extension and generalization of Inverse Rayleigh distribution were studied by some authors. [9] studied some properties of Exponentiated Transmuted Generalized Rayleigh distribution, [10] proposed Half-Logistics Inverse Rayleigh distribution, [11] studied type II Topp-Leone inverse Rayleigh distribution, [12] Transmuted inverse Rayleigh distribution (TIR), [13] fitted the same data on odd Frechet inverse Rayleigh distribution (OFIR) and one parameter Inverse Rayleigh distribution. The possibility of using inverse Rayleigh distribution in this regard has not been accessed.…”

Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

“…In recent years, a number of extensions for the IR distribution have been developed using different methods of generalization by several authors, see, for example, beta IR distribution (Leao et al;, transmuted IR (TIR) distribution (Ahmed et al 2014), modified IR (MIR) distribution (Khan;2014), transmuted modified IR (TMIR) distribution (Khan and King; transmuted exponentiated IR (TEIR) distribution , Kumaraswamy exponentiated IR (KEIR) distribution 2016), weighted IR distribution (Fatima and Ahmad;2017) and odd Fréchet IR distribution (Elgarhy and Alrajhi;2018).…”