Research Article
Exponentiated Inverse Unit Teissier Distribution and Its Application to Survival Data
John Kimani*
,
Nicholas Makumi,
Kilai Mutua
Issue:
Volume 15, Issue 4, August 2026
Pages:
112-132
Received:
26 May 2026
Accepted:
7 July 2026
Published:
7 July 2026
DOI:
10.11648/j.ajtas.20261504.11
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Abstract: Probability distribution theory is fundamental to statistical modeling, especially in survival analysis, where correct representation of time-to-event data is critical. Classical distributions such as the Weibull and exponential have been used with great success but fall behind in modeling complex datasets with heavy-tailed behavior. The Inverse Unit Teissier Distribution (IUTD) presents a good solution to the issue; however, it is one-parameter-tailed. The authors introduced a new distribution called the Exponentiated Inverse Unit Teissier Distribution (EIUTD) as a modification of the IUTD to tackle the single-parameter constraint by incorporation of a shape parameter via exponentiation of the baseline IUTD. The present work developed the cumulative distribution function (CDF) and probability density function (PDF) of the EIUTD in a systematic way, investigated its statistical properties such as moments, quantile function, order statistics, Shannon and Renyi entropy, and skewness and kurtosis, estimated parameters using Maximum Likelihood Estimation (MLE), and performed simulation studies that showed the consistency and efficiency of the estimators for different sample sizes. The modeling capability exhibited by the EIUTD model across two different public health applications confirmed its strong performance. For the Kenya DHS 2022 child mortality data set (n = 77), the EIUTD produced a substantially better statistical fit than the IUTD base model with respect to both AIC (529.19 vs. 653) and BIC (533.88 vs. 655.35 ), while demonstrating acceptable goodness-of-fit based on the Kolmogorov-Smirnov test (KS p = 0.1289). For the COVID-19 recovery times of vaccinated individuals in Kenya (n = 107), the EIUTD model provided competitive performance (AIC = 471.96, p = 0.1825) when compared with both the Lognormal and Gamma models and additionally provided a clearer hazard interpretation via the α-β parameterization than either of the other models. The overall flexible parameterization capability offered by the EIUTD model suggests that it is an appropriate survival analysis method for demographic health research and also for infectious disease epidemiology.
Abstract: Probability distribution theory is fundamental to statistical modeling, especially in survival analysis, where correct representation of time-to-event data is critical. Classical distributions such as the Weibull and exponential have been used with great success but fall behind in modeling complex datasets with heavy-tailed behavior. The Inverse Un...
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