Abstract
A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied as an extension of the half-logistic inverse Rayleigh model. The sine half-logistic inverse Rayleigh model is a new inverse Rayleigh distribution extension. In the application section, we show that the sine half-logistic inverse Rayleigh distribution is more flexible than the half-logistic inverse Rayleigh and inverse Rayleigh distributions. The statistical properties of the half-logistic inverse Rayleigh model are calculated, including the quantile function, moments, moment generating function, incomplete moment, and Lorenz and Bonferroni curves. Entropy measures such as Rényi entropy, Havrda and Charvat entropy, Arimoto entropy, and Tsallis entropy are proposed for the sine half-logistic inverse Rayleigh distribution. To estimate the sine half-logistic inverse Rayleigh distribution parameters, statistical inference using the maximum likelihood method is used. Applications of the sine half-logistic inverse Rayleigh model to real datasets demonstrate the flexibility of the sine half-logistic inverse Rayleigh distribution by comparing it to well-known models such as half-logistic inverse Rayleigh, type II Topp–Leone inverse Rayleigh, transmuted inverse Rayleigh, and inverse Rayleigh distributions.
Highlights
Inverse and half-inverse problems are studied in general operator theory [1,2,3], and many statisticians are focusing on generated families of distributions such as Kumaraswamy-G [4], T-X family [5], sine-G [6], type II half logistic-G [7], Weibull-G [8], the Burr type X-G [9], a new power Topp–Leone-G [10], truncated Cauchy power-G [11], beta generalized Marshall–Olkin–Kumaraswamy-G [12], transmuted odd Frechet-G [13], new Kumaraswamy-G [14], Kumaraswamy Kumaraswamy-G [15], generalized Kumaraswamy-G [16], sine Topp–Leone-G [17], generalized transmuted exponentiated G [18], and Kumaraswamy transmuted-G [19]
Several authors have developed a number of extensions for the inverse Rayleigh (IR) distribution in recent years, using various methods of generalization (see, for example, beta IR in [20], transmuted IR (TIR) in [21], modified IR in [22], transmuted modified IR in [23], Kumaraswamy exponentiated IR in [24], weighted IR in [25], odd Frechet IR in [26], and half-logistic IR (HLIR) in [27])
We present the sine half-logistic IR (SHLIR) distribution, a new lifetime model with two parameters
Summary
Inverse and half-inverse problems are studied in general operator theory [1,2,3], and many statisticians are focusing on generated families of distributions such as Kumaraswamy-G [4], T-X family [5], sine-G [6], type II half logistic-G [7], Weibull-G [8], the Burr type X-G [9], a new power Topp–Leone-G [10], truncated Cauchy power-G [11], beta generalized Marshall–Olkin–Kumaraswamy-G [12], transmuted odd Frechet-G [13], new Kumaraswamy-G [14], Kumaraswamy Kumaraswamy-G [15], generalized Kumaraswamy-G [16], sine Topp–Leone-G [17], generalized transmuted exponentiated G [18], and Kumaraswamy transmuted-G [19]. Several authors have developed a number of extensions for the IR distribution in recent years, using various methods of generalization (see, for example, beta IR in [20], transmuted IR (TIR) in [21], modified IR in [22], transmuted modified IR in [23], Kumaraswamy exponentiated IR in [24], weighted IR in [25], odd Frechet IR in [26], and half-logistic IR (HLIR) in [27]). We present the sine half-logistic IR (SHLIR) distribution, a new lifetime model with two parameters.
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