Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Hassan, Amal S.; Assar, Salwa M.; Abdelghaffar, Ahmed M.

doi:10.21307/stattrans-2020-046

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…Reference [15] discussed the Weibull I Lomax model. Reference [16] suggested the power transmuted I Rayleigh model. Reference [17] investigated the I Topp-Leone distribution, and half logistic I Topp-Leone distribution was studied in [18].…”

Section: Introductionmentioning

confidence: 99%

Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

Almutiry

2021

Journal of Mathematics

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This research article proposes a new probability distribution, referred to as the inverted length-biased exponential distribution. The hazard rate function (HZRF) and density function (PDF) in the new distribution allow additional flexibility as well as some desired features. It provides a more flexible approach that may be used to represent many forms of real-world data. The quantile function (QuF), moments (MOs), moment generating function (MOGF), mean residual lifespan (MRLS), mean inactivity time (MINT), and probability weighted moments (PRWMOs) are among the mathematical and statistical features of the inverted length-biased exponential distribution. In the case of complete and type II censored samples (TIICS), the maximum likelihood (MLL) strategy can be used to estimate the model parameters. An asymptotic confidence interval (COI) of parameter is constructed at two confidence levels. We perform simulation study to examine the accuracy of estimates depending upon some statistical measures. Simulation results show that there is great agreement between theoretical and empirical studies. We demonstrate the new model’s relevance and adaptability by modeling three lifespan datasets. The proposed model is a better fit than the half logistic inverse Rayleigh (HLOIR), type II Topp–Leone inverse Rayleigh (TIITOLIR), and transmuted inverse Rayleigh (TRIR) distributions. We anticipate that the expanded distribution will attract a broader range of applications in a variety of fields of research.

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Section: Introductionmentioning

confidence: 99%

Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

Almutiry

2021

Journal of Mathematics

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“…kδ m e e−1 i . Inserting (30) into (29), then the cumulative residual Rényi entropy of the KMPTL distribution is…”

Section: Cumulative Residual Rényi Entropymentioning

confidence: 99%

“…In recent years, many authors used the power transformation technique to obtain statistical distributions that are more flexible due to the shape parameter. Several of the potential power distributions are as follows: the power Zeghdoudi distribution [26], power modified Kies distribution [27], power Darna distribution [28], power Burr X distribution [29], power transmuted inverse Rayleigh distribution [30], power Rama distribution [31], power binomial exponential distribution [32], power Aradhana distribution [33], power Lomax distribution [34], power half logistic distribution [35], power Shanker distribution [36], power Lindley distribution [37], and power Cauchy distribution [38], among others.…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

Alotaibi

Al-Moisheer

Elbatal

et al. 2023

Axioms

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In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets.

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“…It is seen from tables that the estimators of θ (for = 0.5 and 2) as increases and the results n increases for complete samples are slightly better than the corresponding results for Type II censored samples. [1][2][3][4][5][6][7][8][9][10] Soliman et al (2010) are shown that numerical results of the Bayesian predictive interval for several values of different prior parameters will be obtained. The calculations are carried out according to the following steps: (1) For given values of the inverse Rayleigh parameters θ generate a random variable X from the inverse Rayleigh distribution (1.1) and selected the first 10 records.…”

Section: Simulation Studymentioning

confidence: 99%

Untitled

2022

AJMS

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This article discusses Bayesian and non-Bayesian estimation problem of the unknown parameter for the inverse Rayleigh distribution based on the lower record values. Maximum likelihood estimators of the unknown parameters were obtained. Furthermore, Bayes estimator has been developed under squared error and zero one loss functions. We discuss also statistical properties and estimation of power-transmuted inverse Rayleigh distribution (EIRD). We introduce the transmuted modified inverse Rayleigh distribution using quadratic rank transmutation map, which extends the modified inverse Rayleigh distribution. We introduce a generalization of the inverse Rayleigh distribution known as EIRD which extends a more flexible distribution for modeling life data. Some statistical properties of the EIRD are investigated, such as mode, quantiles, moments, reliability, and hazard function. We describe different methods of parametric estimations of EIRD discussed by using maximum likelihood estimators, percentile-based estimators, least squares estimators, and weighted least squares estimators and compare those estimates using extensive numerical simulations. The new two-scale parameters generalized distribution were studies with its distribution and density functions, besides that the basic properties such as survival, hazard, cumulative hazard, quantile function, skewness, and Kurtosis functions were established and derived. To estimate the model parameters, maximum likelihood, and rank set sampling estimation methods were applied with reallife data. We have introduced weighted inverse Rayleigh (WIR) distribution and investigated its different statistical properties. Expressions for the Mode and entropy have also been derived. A comprehensive account of the mathematical properties of the modified inverse Rayleigh distribution including estimation and simulation with its reliability behavior is discussed.

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Statistical Properties and Estimation of Power-Transmuted Inverse Rayleigh Distribution

Cited by 8 publications

References 11 publications

Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

Inverted Length-Biased Exponential Model: Statistical Inference and Modeling

Bayesian and Non-Bayesian Estimation for a New Extension of Power Topp–Leone Distribution under Ranked Set Sampling with Applications

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