The Beta-Modified Weighted Rayleigh Distribution: Application to Virulent Tubercle Disease

Abstract

Flexible parametric models are useful for modeling survival data and this has become an important field in statistics; and concern of statisticians in data analysis. Therefore, this paper presents a univariate model called Beta modified weighted Rayleigh distribution constructed from modified weighted Rayleigh distribution. The new distribution is achieved by introducing two shape parameters to the existing modified Weighted Rayleigh distribution using logit of beta function. The idea is to verify if the Beta modified Weighted Rayleigh distribution would perform better than modified Weighted Rayleigh distribution in modeling survival data. The statistical properties such as; survival rate, hazard rate, moment generating functions, skewness and kurtosis are determined for the new distribution. We also performed the expected estimation of model parameters by maximum likelihood. The Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC) and Consistent Akaike Information Criterion (CAIC) are employed to select the best model. The superiority and flexibility of the proposed distribution is illustrated and applied to survival times of guinea pigs with virulent tubercle data sets. The results with the baseline distribution are also compared. Likewise, results from the model
selection criteria: the AIC, BIC and CAIC favoured BMWR; indicating that the proposed distribution performs and has better representation of the data than the MWR distribution.