A new weighted version of alpha power transformation method: properties and applications to COVID-19 and software reliability data

2021 ◽  
Author(s):  
Refah Alotaibi ◽  
Hassan Okasha ◽  
Hoda Rezk ◽  
Mazen Nassar
Author(s):  
Mohamed E. Mead ◽  
Gauss M. Cordeiro ◽  
Ahmed Z. Afify ◽  
Hazem Al Mofleh

Mahdavi A. and Kundu D. (2017) introduced a family for generating univariate distributions called the alpha power transformation. They studied as a special case the properties of the alpha power transformed exponential distribution. We provide some mathematical properties of this distribution and define a four-parameter lifetime model called the alpha power exponentiated Weibull distribution. It generalizes some well-known lifetime models such as the exponentiated exponential, exponentiated Rayleigh, exponentiated Weibull and Weibull distributions. The importance of the new distribution comes from its ability to model monotone and non-monotone failure rate functions, which are quite common in reliability studies. We derive some basic properties of the proposed distribution including quantile and generating functions, moments and order statistics. The maximum likelihood method is used to estimate the model parameters. Simulation results investigate the performance of the estimates. We illustrate the importance of the proposed distribution over the McDonald Weibull, beta Weibull, modified Weibull, transmuted Weibull and exponentiated Weibull distributions by means of two real data sets.


2018 ◽  
Vol 5 (3) ◽  
pp. 421-436 ◽  
Author(s):  
M. Nassar ◽  
A. Alzaatreh ◽  
O. Abo-Kasem ◽  
M. Mead ◽  
M. Mansoor

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 581 ◽  
Author(s):  
Sushant Mehan ◽  
Margaret Gitau ◽  
Dennis Flanagan

Modeling efforts to simulate hydrologic processes under different climate conditions rely on accurate input data. Among other inaccuracies, errors in climate projections can lead to incorrect decisions. This study aimed to develop a reliable climate (precipitation and temperature) database for the Western Lake Erie Basin for the 21st century. Two statistically downscaled bias-corrected sources of climate projections (GDO: Global Downscaled Climate and Hydrology Projections and MACA: Multivariate Adaptive Constructed Analogs) were tested for their effectiveness in simulating historic climate (1966–2005) using ground-based station data from the National Climatic Data Center. MACA was found to have less bias than GDO and was better at simulating selected climate indices; thus, its climate projections were subsequently tested with different bias correction methods including the power transformation method, variance scaling of temperature, and Stochastic Weather Generators. The power transformation method outperformed the other methods and was used in bias corrections for 2006 to 2099. From the analysis, mean daily precipitation values were expected to remain more or less the same under both RCP (Representative Concentration Pathway) 4.5 and RCP 8.5 scenarios, ranging between 2.4 mm and 3.2 mm, while standard deviations were expected to increase, pointing to a rescaling of the distribution. Maximum one-day precipitation was expected to increase and could vary between 120 and 650 mm across the basin, while the number of wet days could potentially increase under the effects of RCP 4.5 and RCP 8.5. Both mean maximum and mean minimum daily air temperatures were expected to increase by up to 5.0 °C across the basin, while absolute maximum and minimum values could increase by more than 10 °C. The number of days in which precipitation could potentially fall as snow was expected to decrease, as was the annual number of days for optimal corn growth, although an earlier start to the growing season could be expected. Results from this study were very useful in creating a reliable climate database for the entire Western Lake Erie Basin (WLEB), which can be used for hydrologic, water resources, and other applications in the basin. The resulting climate database is published and accessible through the Purdue University Research Repository (Mehan et al., 2019), which is an open-access repository.


Proceedings ◽  
2019 ◽  
Vol 27 (1) ◽  
pp. 32 ◽  
Author(s):  
Švantner ◽  
Muzika ◽  
Houdková

Thermographic testing is an inspection method, which primary indicates a presence of discontinuities in a tested sample. Its application to coatings can indicate a presence of local thickness variations; however, it mostly does not bring a quantitative information about a thickness of the coatings. This contribution is focused on a quantification of the thermographic inspection, which would make possible an evaluation of coating thickness differences. A flash pulse thermographic testing was applied to thermally sprayed coatings. An importance of a precise synchronization of a flash-source and thermographic recording was determined. Different evaluation methods were analyzed and their comparison showed that a time-power transformation method is the most suitable for a quantification of the inspection results.


2020 ◽  
Vol 9 (6) ◽  
pp. 90
Author(s):  
A. A. Ogunde ◽  
S. T. Fayose ◽  
B. Ajayi ◽  
D. O. Omosigho

In this work, we introduce a new generalization of the Inverted Weibull distribution called the alpha power Extended Inverted Weibull distribution using the alpha power transformation method. This approach adds an extra parameter to the baseline distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and moment generating functions, reliability analysis, Lorenz and Bonferroni and curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Simulation method and three real life data sets are presented to demonstrate the effectiveness of the new model.


2018 ◽  
Author(s):  
Sushant Mehan ◽  
Margaret W. Gitau ◽  
Dennis C. Flanagan

Abstract. Modeling efforts to simulate hydrologic processes under different climate conditions rely on accurate input data; inaccuracies in climate projections can lead to incorrect decisions. This study aimed to develop a reliable climate (precipitation and temperature) database for the Western Lake Erie Basin (WLEB) for the 21st century. Two statistically downscaled bias-corrected sources of climate projections (GDO and MACA) were tested for their effectiveness in simulating historic climate (1966–2005) using ground-based station data from the National Climatic Data Center (NCDC). MACA was found to have less bias than GDO and was better in simulating certain climate indices, thus, its climate projections were subsequently tested with different bias correction methods including the power transformation method, variance scaling of temperature, and Stochastic Weather Generators. The power transformation method outperformed the other methods and was used in bias corrections for 2006 to 2099. From the analysis, maximum one-day precipitation could vary between 120 and 650 mm across the basin, while the number of days with no precipitation could reduce by 5–15 % under the RCP 4.5 and RCP 8.5. The number of wet sequences could increase up to 9 times and the conditional probability of having a wet day followed by wet day could decrease by 25 %. The maximum and minimum daily air temperatures could increase by 2–12 % while the annual number of days for optimal corn growth could decrease by 0–10 days. The resulting climate database will be made accessible through an open-access platform.


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