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# Estimating the Parameters of Exponential-Rayleigh Distribution under Type-I Censored Data

## Authors

• Rihaam N Shatti Department of Mathematics, College of Science for women, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-5015-4847
• Iden H. Al-Kinani Department of Mathematics, College of Science for women, University of Baghdad, Baghdad, Iraq

## Keywords:

COVID-19, Exponential-Rayleigh distribution (ER), Hazard function, Singly type one censored data, Survival function

## Abstract

This paper discusses estimating the two scale parameters of Exponential-Rayleigh distribution for singly type one censored data which is one of the most important Rights censored data, using the maximum likelihood estimation method (MLEM) which is one of the most popular and widely used classic methods, based on an iterative procedure such as the Newton-Raphson to find estimated values for these two scale parameters by using real data for COVID-19 was taken from the Iraqi Ministry of Health and Environment, AL-Karkh General Hospital. The duration of the study was in the interval 4/5/2020 until 31/8/2020 equivalent to 120 days, where the number of patients who entered the (study) hospital with sample size is (n=785). The number of patients who died during the period of study was (m=88). And the number of patients who survived during the study period was (n-m=697), then utilized one of the most important non-parametric tests which is the Chi-square test to determine if the sample (data) corresponded with the Exponential-Rayleigh distribution (ER). then, after estimating the parameters of ER distribution for singly type-I censoring data, compute the survival function, hazard function, and probability density function.

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