A Two-Parameter Model: Properties and Estimation under Ranked Sampling

Rashad Bantan, Mahmoud Elsehetry, Amal S. Hassan, Mohammed Elgarhy, Dreamlee Sharma, Christophe Chesneau and Farrukh Jamal
Additional contact information
Rashad Bantan: Deanship of Scientific Research, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Mahmoud Elsehetry: Deanship of Information Technology, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Amal S. Hassan: Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
Mohammed Elgarhy: The Higher Institute of Commercial Sciences, Al Mahalla Al Kubra, Algharbia 31951, Egypt
Dreamlee Sharma: Department of Mathematics, Adamas University, Kolkata 700020, India
Christophe Chesneau: Department of Mathematics, LMNO, University of Caen, CEDEX, 14032 Caen, France
Farrukh Jamal: Department of Statistics, The Islamia University of Bahawalpur, Punjab 63100, Pakistan

Mathematics, 2021, vol. 9, issue 11, 1-16

Abstract: This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions.

Keywords: type II half-logistic–G class; inverted Topp–Leone distribution; maximum likelihood method; ranked set sampling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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