The Gamma1-Epsilon Distribution: Its Statistical Properties and Applications
Isaac Esbond Gongsin,
Funmilayo Westnand Oshogboye Saporu
Issue:
Volume 6, Issue 4, December 2020
Pages:
65-70
Received:
4 September 2020
Accepted:
24 September 2020
Published:
17 October 2020
Abstract: The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed based on the gamma type-I generator, called the gamma1-epsilon distribution. Its statistical properties are described. The area under the curve of the density plots is shown through numerical integration to equal one with very minimal error margins. The density plots show shapes that are similar to many standard lifetime distributions. This implies that it is flexible to assume different shapes that can model many different random phenomena. Its hazard rate function plots also show varying shapes, namely J-shaped and bathtub-shaped, that indicate its possible use as a model for the study of survival life of biological organisms, electrical and mechanical components. The distribution is applied to the time to death of women with temporary disabilities, remission time of cancer patients and wind speed. The fits to these datasets are good with precise parameter estimates. Its compatibility with data from these dissimilar processes shows it holds a good prospect for real life application.
Abstract: The construction of new probability distributions is an active field of research. It provides the opportunity for dynamic system modelers to choose the best model from a plethora of probability distributions that provide good fit to some data set using model selection criteria. In this study a new probability distribution function is constructed ba...
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The Characteristic Property of Five Parameter Type II Generalized Logistic Distribution
Sule Ibrahim,
Olalekan Akanji Bello,
Awodutire Phillip Oluwatobi,
Hammed Olanrewaju Lawal
Issue:
Volume 6, Issue 4, December 2020
Pages:
71-74
Received:
29 October 2016
Accepted:
3 December 2016
Published:
25 December 2020
Abstract: Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized logistic distribution using the probability distribution function and cumulative density function to obtain another five parameter type II generalized logistic distribution which shares the same properties by replacing p with np. We also obtain the quantile function by inverting the cumulative density function of the distribution which can be used to generate random samples arising from the distribution. The survival and hazard functions of the distribution are also obtained.
Abstract: Order statistics are among the most fundamental tools in non-parametric statistics and inference. Special important cases of the order statistics are the minimum and maximum value of a sample, sample median and other sample quantiles. On this note, we obtained the rth minimum and maximum order statistic for the five parameter type II generalized lo...
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