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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:
8 June 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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Research Article
Evaluation of the Quality of Petrol and Natural Gas Fuels
Issue:
Volume 15, Issue 4, August 2026
Pages:
133-140
Received:
12 December 2025
Accepted:
31 December 2025
Published:
11 July 2026
DOI:
10.11648/j.ajtas.20261504.12
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Abstract: Natural gas and gasoline are essential energy sources for transportation and industries worldwide, and their quality is crucial. This study examines a variety of gasoline and natural gas samples to determine which is better based on important factors such sulfur content, firmness, surface tautness, viscidity, and fattening value. Eight different fuel suppliers provided samples, which were tested in violation of established standards such as ISO 8217: 2017 and GSA 141: 2022. Two suppliers' gasoline samples showed densities that were marginally below the allowed limits, indicating possible adulteration with lower-density materials like kerosene. With the exception of one sample, which also displayed increased sulfur levels, surface tension values for almost all samples remained within permissible norms. Viscosity measurements for fuels from three sources were marginally above suggested standards, perhaps leading to improved pollutant emissions, even though all fuels satisfied the minimum calorific value requirements. Only three providers' goods met the maximum allowable limit of 50 ppm in terms of sulfur concentration, meaning that more than 60% of the examined fuel samples had sulfur levels beyond the allowed threshold. These repercussions highlight the need for ongoing monitoring and more stringent quality control throughout the gasoline supply chain in order to guarantee fuel integrity and environmental compliance.
Abstract: Natural gas and gasoline are essential energy sources for transportation and industries worldwide, and their quality is crucial. This study examines a variety of gasoline and natural gas samples to determine which is better based on important factors such sulfur content, firmness, surface tautness, viscidity, and fattening value. Eight different fu...
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Research Article
Modelling the Volatility of the USD/KES Exchange Rate Using the Nadaraya-watson Kernel Regression Estimator
Mary Wangui Wanjohi*,
Josephine Njeri Ngure,
Martin Mutweri Kithinji
Issue:
Volume 15, Issue 4, August 2026
Pages:
141-148
Received:
1 June 2026
Accepted:
10 June 2026
Published:
28 July 2026
DOI:
10.11648/j.ajtas.20261504.13
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Abstract: Exchange rate volatility poses significant challenges for economic planning, risk management, and policy formulation in emerging economies such as Kenya. This study models the volatility of the United States Dollar/ Kenyan Shillings (USD/KES) exchange rate using the nonparametric Nadaraya-Watson kernel regression estimator. Daily buying rates from the Central Bank of Kenya spanning January 2, 2003, to December 29, 2023 (4,764 observations) were used. The Nadaraya-Watson estimator smooths the data using kernel functions and bandwidth parameters, enabling it to adapt to localized features in the volatility pattern that conventional parametric models may overlook. The conditional mean and conditional variance functions were estimated using a Gaussian kernel with cross-validated fixed bandwidths. The optimal bandwidth for the conditional mean was 0.02750928 and for the conditional variance was 0.1349632, with a bandwidth ratio of 4.905869, indicating that the volatility function requires smoother estimation. The conditional variance function exhibited a distinct U-shape, showing higher volatility following extreme positive or negative lagged returns. The model achieved a Root Mean Squared Error (RMSE) of 1.919 for variance, capturing major volatility episodes including the 2008-2009 financial crisis, the 2011 currency crisis, and the 2016 reserves depletion shock. The study concludes that the Nadaraya-Watson kernel regression estimator successfully captures nonlinear volatility dynamics without imposing rigid parametric assumptions, making it suitable for emerging market currencies like the Kenyan shilling.
Abstract: Exchange rate volatility poses significant challenges for economic planning, risk management, and policy formulation in emerging economies such as Kenya. This study models the volatility of the United States Dollar/ Kenyan Shillings (USD/KES) exchange rate using the nonparametric Nadaraya-Watson kernel regression estimator. Daily buying rates from ...
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