Modeling Liver Cancer and Leukemia Data Using Arcsine-Gaussian Distribution

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 distrib...

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Bibliographic Details
Published in:Computers, materials & continua materials & continua, 2021, Vol.67 (2), p.2185-2202
Main Authors: Mohammad A. Alam, Farouq, Alrajhi, Sharifah, Nassar, Mazen, Z. Afify, Ahmed
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Confidence intervals
Estimators
Leukemia
Liver cancer
Normal distribution
Numerical methods
Parameter estimation
Skewed distributions
Statistical analysis
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Summary: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.
ISSN:1546-2226
1546-2218
1546-2226
DOI:10.32604/cmc.2021.015089