Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications

Abstract

This study introduces a new lifetime distribution called the transmuted lower record type inverse Rayleigh which extends the inverse Rayleigh distribution and has the potential to model the recovery times of Covid-19 patients.The new distribution is obtained using the distributions of the first two lower record statistics of the inverse Rayleigh distribution. We discuss some statistical inferences and mathematical properties of the suggested distribution. We examine some characteristics of the proposed distribution such as density shape, hazard function,moments, moment generating function, incomplete moments,Rényi entropy, order statistics, stochastic ordering. We consider five estimation methods such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, Cramér-von Mises for the point estimation of the proposed distribution. Then, a comprehensive Monte Carlo simulation study is carried out to assess the risk behavior of the examined estimators. We provide two real data applications to illustrate the fitting ability of the proposed model, and compare its fit with competitor ones. Unlike many previously proposed distributions, the introduced distribution in this paper has modeled the recovery times of Covid-19 patients.

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

“…When the data on COVID-19 recovery time (dataset 4) were fitted to the GMO-EE distribution, the mean recovery time of male patients aged >60 years was estimated to be 18.35 days. Based on the same dataset, Tanış [ 47 ] estimated the mean recovery time to be about 21 days, while Voinsky et al [ 48 ] reported an average recovery time of approximately 15 days for another sample of male COVID-19 patients over the age of 60 years (n = 582) and Barman et al [ 49 ] obtained the 95% confidence interval for average recovery time of 16 to 34 days based on another sample of COVID-19 patients (n = 221). The probability of recovery within 2 weeks was calculated as 44.62% based on the GMO-EE distribution, while Tanış [ 47 ] found it to be 45.25%.…”

“…Based on the same dataset, Tanış [ 47 ] estimated the mean recovery time to be about 21 days, while Voinsky et al [ 48 ] reported an average recovery time of approximately 15 days for another sample of male COVID-19 patients over the age of 60 years (n = 582) and Barman et al [ 49 ] obtained the 95% confidence interval for average recovery time of 16 to 34 days based on another sample of COVID-19 patients (n = 221). The probability of recovery within 2 weeks was calculated as 44.62% based on the GMO-EE distribution, while Tanış [ 47 ] found it to be 45.25%. The results obtained from the GMO-EE distribution are thus supported by the findings of previous studies.…”

“…The fourth real dataset includes recovery times of survivors as measured from the first positive COVID-19 PCR test to the first negative test for 50 males over 60 years old. This dataset was obtained from anonymized data published by the Israeli Ministry of Health and it was analyzed in a previous work [47]. The dataset contains the following values: 16, 16, 16, 14, 36, 9, 10, 11, 8, 9, 12, 10, 22, 5, 11, 17, 20, 12, 29, 12, 15, 25, 25, 24, 18, 13, 44, 14, 20, 19, 11, 10, 18, 21, 31, 9, 29, 12, 10, 10, 13, 12, 19, 33, 37, 16, 63, 9, 28, and 16. We analyze this dataset to compare the GMO-EE with the W, EE [24], MOEBXII [41], GBE-II [42], EOWEx [18], EWP [12], and exponential distributions.…”

A new Lifetime Distribution Based on the Transmuted First Two Lower Records

“…Both in terms of distribution properties and statistical inference parallel to the study [11]. Tanış et al [13], introduced a transmutation lower record type and suggested a sub-model for Fréchet distribution, moreover Tanış [14], suggested transmutation lower record type inverse Rayleigh and Tanış [15], suggested transmutation lower record type power function distribution.…”