New Statistical Approaches for Modeling the COVID‐19 Data Set: A Case Study in the Medical Sector

Abstract

Statistical distributions have great applicability for modeling data in almost every applied sector. Among the available classical distributions, the inverse Weibull distribution has received considerable attention. In the practice of distribution theory, numerous methods have been studied and suggested/introduced to increase the flexibility level of the traditional probability distributions. In this paper, we implement different distribution methods to obtain five new different versions of the inverse Weibull model. The new modifications of the inverse Weibull model are called the logarithm transformed-inverse Weibull, a flexible reduced logarithmic-inverse Weibull, the weighted TX-inverse Weibull, a new generalized-inverse Weibull, and the alpha power transformed extended-inverse Weibull distributions. To illustrate the flexibility and applicability of the new modifications of the inverse Weibull model, a biomedical data set is analyzed. The data set consists of 108 observations and represents the mortality rate of the COVID-19-infected patients. The practical application shows that the new generalized-inverse Weibull is the best modification of the inverse Weibull distribution.

Properties, Quantile Regression, and Application of Bounded Exponentiated Weibull Distribution to COVID- 19 Data of Mortality and Survival Rates

“…𝜶 (1) 𝐟(𝐲) = 𝜶𝛌𝛃𝒆 −(𝛌𝐲) 𝜷 [𝟏 − 𝒆 −(𝛌𝐲) 𝜷 ] 𝜶−𝟏 (2) Now, a distribution termed as the Bound Exponentiated Weibull Distribution (BEWD) is developed following the conversion of 𝑒 −𝑋 = Y → −ln(Y) = X. The CDF of the BEWD is as follows, 𝐹 𝑌 (𝑦; λ, 𝛼, 𝛽) = P(𝑒 −𝑋 ≤ 𝑦) , 𝐹 𝑌 (𝑦; λ, 𝛼, 𝛽) = P(−X ≤ ln(Y)), 𝐹 𝑌 (𝑦; λ, 𝛼, 𝛽) = P(X ≤ −ln(Y)), or 𝐹 𝑌 (𝑦; λ, 𝛼, 𝛽) = 1 − 𝐹 𝑋 (− ln(Y) ; λ, 𝛼).…”

A New Family of Heavy-Tailed Generalized Topp-Leone-G Distributions with Application

“…These data are recorded between March 4, 2022, and July 20, 2020. The considered data set was analyzed by Almazah et al (2022), has one hundred and eight observations and is given in the appendix. The data analysis results given in Table 6 indicates that the HT-GEN-TL-LLoG distribution outperforms the other fitted distributions since it has the lowest values of the goodness-of-fit statistics: −2 ln(L), AIC,CAIC, BIC,W * , A * , K −S and largest p-value of the K − S statistic.…”

Properties, quantile regression, and application of bounded exponentiated Weibull distribution to COVID-19 data of mortality and survival rates

“…These advancements are expected to have a profound impact on the fields of engineering, economics, psychology, and biology, enabling more accurate and effective analysis of data involving ratios, rates, and percentages within the unit interval [0, 1]. Nasiru et al 8 introduced a new lifetime distribution named as bounded truncated Cauchy power exponential distribution to model the unit data, Almazah et al 9 executed various distribution methods to find five new different forms of the inverse Weibull model and the resultant models applied on the mortality rate of COVID-19. Moraes-Rego 10 introduced a unit interval distribution named a truncated exponentiated exponential distribution.…”