Open Access

ARTICLE

Modeling Liver Cancer and Leukemia Data Using Arcsine-Gaussian Distribution

Farouq Mohammad A. Alam¹, Sharifah Alrajhi¹, Mazen Nassar^1,2, Ahmed Z. Afify^3,*

1 Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia
2 Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig, 44511, Egypt
3 Department of Statistics, Mathematics and Insurance, Benha University, Benha, 13511, Egypt

* Corresponding Author: Ahmed Z. Afify. Email:

(This article belongs to the Special Issue: Artificial Intelligence and IoT based intelligent systems using high performance computing for Medical applications.)

Computers, Materials & Continua 2021, 67(2), 2185-2202. https://doi.org/10.32604/cmc.2021.015089

Received 06 November 2020; Accepted 12 December 2020; Issue published 05 February 2021

Abstract

The main objective of this paper is to discuss a general family of distributions generated from the symmetrical arcsine distribution. The considered family includes various asymmetrical and symmetrical probability distributions as special cases. A particular case of a symmetrical probability distribution from this family is the Arcsine–Gaussian distribution. Key statistical properties of this distribution including quantile, mean residual life, order statistics and moments are derived. The Arcsine–Gaussian parameters are estimated using two classical estimation methods called moments and maximum likelihood methods. A simulation study which provides asymptotic distribution of all considered point estimators, 90% and 95% asymptotic confidence intervals are performed to examine the estimation efficiency of the considered methods numerically. The simulation results show that both biases and variances of the estimators tend to zero as the sample size increases, i.e., the estimators are asymptotically consistent. Also, when the sample size increases the coverage probabilities of the confidence intervals increase to the nominal levels, while the corresponding length decrease and approach zero. Two real data sets from the medicine filed are used to illustrate the flexibility of the Arcsine–Gaussian distribution as compared with the normal, logistic, and Cauchy models. The proposed distribution is very versatile to fit real applications and can be used as a good alternative to the traditional gaussian distribution.

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Keywords

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