# Length Biased Burr- XII Distribution: Properties and Application

## Authors

• Abd-Elfattah A. M Department of MathematicalStatistics, Institute of Statistical Studies & Research, Cairo University,
• Mahdy .M Department of Statistics, Mathematics and Insurance,Benha University, Egypt.
• Ismail .G Ministry of Insurance and Pensions

## Keywords:

Burr XII distribution, Length Biased, Survival Function, Order Statistics, Renei Entropy, Maximum Likelihood Method

## Abstract

Burr XII distribution is widely applicable in reliability and life testing problems in engineering as well as in survival analysis. The concept of weighted and size- biased sampling and length biased  distribution due to importance of this kind of distributions and it's application  in many fields such as medicine, ecology, reliability and human populations. In this paper, length biased Burr XII  distribution is proposed and studied. Different properties of this new distribution are discussed such as the density function and its behaviour , moments, hazard , survival functions and order statistics. The parameters of this new distribution are estimated by maximum likelihood method . The observed information matrix is derived. Finally, we provide a simulation and real data analysis to see how the new model is applicable in practice.

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2021-02-25

## How to Cite

A. M, A.-E., .M, M., & .G, I. (2021). Length Biased Burr- XII Distribution: Properties and Application. International Journal of Sciences: Basic and Applied Research (IJSBAR), 56(1), 222–244. Retrieved from https://www.gssrr.org/index.php/JournalOfBasicAndApplied/article/view/12165

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