scholarly journals Bayesian and Classical Inference for the Generalized Log-Logistic Distribution with Applications to Survival Data

2021 ◽  
Vol 2021 ◽  
pp. 1-24
Author(s):  
Abdisalam Hassan Muse ◽  
Samuel Mwalili ◽  
Oscar Ngesa ◽  
Saad J. Almalki ◽  
Gamal A. Abd-Elmougod
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Survival Data ◽  
Hazard Rate ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Data Set ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Highest Posterior Density

The generalized log-logistic distribution is especially useful for modelling survival data with variable hazard rate shapes because it extends the log-logistic distribution by adding an extra parameter to the classical distribution, resulting in greater flexibility in analyzing and modelling various data types. We derive the fundamental mathematical and statistical properties of the proposed distribution in this paper. Many well-known lifetime special submodels are included in the proposed distribution, including the Weibull, log-logistic, exponential, and Burr XII distributions. The maximum likelihood method was used to estimate the unknown parameters of the proposed distribution, and a Monte Carlo simulation study was run to assess the estimators’ performance. This distribution is significant because it can model both monotone and nonmonotone hazard rate functions, which are quite common in survival and reliability data analysis. Furthermore, the proposed distribution’s flexibility and usefulness are demonstrated in a real-world data set and compared to its submodels, the Weibull, log-logistic, and Burr XII distributions, as well as other three-parameter parametric survival distributions, such as the exponentiated Weibull distribution, the three-parameter log-normal distribution, the three-parameter (or the shifted) log-logistic distribution, the three-parameter gamma distribution, and an exponentiated Weibull distribution. The proposed distribution is plausible, according to the goodness-of-fit, log-likelihood, and information criterion values. Finally, for the data set, Bayesian inference and Gibb’s sampling performance are used to compute the approximate Bayes estimates as well as the highest posterior density credible intervals, and the convergence diagnostic techniques based on Markov chain Monte Carlo techniques were used.

scholarly journals Global and regional performances of SPI candidate distribution functions in observations and simulations

2020 ◽  
Author(s):  
Patrick Pieper ◽  
André Düsterhus ◽  
Johanna Baehr
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Weibull Distribution ◽  
Standardized Precipitation Index ◽  
Distribution Functions ◽  
Monthly Precipitation ◽  
Precipitation Data ◽  
Data Set ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull

Abstract. The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within literature. This study illuminates the long-standing dispute and proposes a solution which ensures the normality of the index for all common accumulation periods in observations and simulations. We compare the normality of SPI time-series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison evaluates actual against theoretical occurrence probabilities of SPI categories, and the quality of the fit of candidate distribution functions against their complexity with Akaike's Information Criterion. SPI time-series, spanning 1983–2013, are calculated from Global Precipitation Climatology Project's monthly precipitation data-set and seasonal precipitation hindcasts from the Max Planck Institute Earth System Model. We evaluate these SPI time-series over the global land area and for each continent individually during winter and summer. While focusing on an accumulation period of 3-months, we additionally test the drawn conclusions for other common accumulation periods (1-, 6-, 9-, and 12-months). Our results suggest to exercise caution when using the gamma distribution to calculate SPI; especially in simulations or their evaluation. Further, our analysis shows a distinctly improved normality for SPI time-series derived with the exponentiated Weibull distribution relative to other distributions. The use of the exponentiated Weibull distribution maximizes the normality of SPI time-series in observations and simulations both individual as well as concurrent. Its use further maximizes the normality of SPI time-series over each continent and for every investigated accumulation period. We, therefore, advocate to derive SPI with the exponentiated Weibull distribution, irrespective of the heritage of the precipitation data or the length of analyzed accumulation periods.

scholarly journals Bayesian Estimation and Prediction for Flexible Weibull Model under Type-II Censoring Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Vikas Kumar Sharma
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Bayesian Estimation ◽  
Model Parameters ◽  
Type Ii ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Type Ii Censoring ◽  
Highest Posterior Density ◽  
Censoring Scheme

We have developed the Bayesian estimation procedure for flexible Weibull distribution under Type-II censoring scheme assuming Jeffrey's scale invariant (noninformative) and Gamma (informative) priors for the model parameters. The interval estimation for the model parameters has been performed through normal approximation, bootstrap, and highest posterior density (HPD) procedures. Further, we have also derived the predictive posteriors and the corresponding predictive survival functions for the future observations based on Type-II censored data from the flexible Weibull distribution. Since the predictive posteriors are not in the closed form, we proposed to use the Monte Carlo Markov chain (MCMC) methods to approximate the posteriors of interest. The performance of the Bayes estimators has also been compared with the classical estimators of the model parameters through the Monte Carlo simulation study. A real data set representing the time between failures of secondary reactor pumps has been analysed for illustration purpose.

Global and regional performances of SPI candidate distribution functions in observations and simulations

2020 ◽  
Author(s):  
Patrick Pieper ◽  
André Düsterhus ◽  
Johanna Baehr
Keyword(s):  
Time Series ◽  
Distribution Function ◽  
Weibull Distribution ◽  
Standardized Precipitation Index ◽  
Distribution Functions ◽  
Monthly Precipitation ◽  
Precipitation Data ◽  
Data Set ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull

<p>The Standardized Precipitation Index (SPI) is a widely accepted drought index. Its calculation algorithm normalizes the index via a distribution function. Which distribution function to use is still disputed within literature. This study illuminates the long-standing dispute and proposes a solution which ensures the normality of the index for all common accumulation periods in observations and simulations.</p><p>We compare the normality of SPI time-series derived with the gamma, Weibull, generalized gamma, and the exponentiated Weibull distribution. Our normality comparison evaluates actual against theoretical occurrence probabilities of SPI categories, and the quality of the fit of candidate distribution functions against their complexity with Akaike's Information Criterion. SPI time-series, spanning 1983–2013, are calculated from Global Precipitation Climatology Project's monthly precipitation data-set and seasonal precipitation hindcasts from the Max Planck Institute Earth System Model. We evaluate these SPI time-series over the global land area and for each continent individually during winter and summer. While focusing on an accumulation period of 3-months, we additionally test the drawn conclusions for other common accumulation periods (1-, 6-, 9-, and 12-months).</p><p>Our results suggest to exercise caution when using the gamma distribution to calculate SPI; especially in simulations or their evaluation. Further, our analysis shows a distinctly improved normality for SPI time-series derived with the exponentiated Weibull distribution relative to other distributions. The use of the exponentiated Weibull distribution maximizes the normality of SPI time-series in observations and simulations both individual as well as concurrent. Its use further maximizes the normality of SPI time-series over each continent and for every investigated accumulation period. We, therefore, advocate to derive SPI with the exponentiated Weibull distribution, irrespective of the heritage of the precipitation data or the length of analyzed accumulation periods.</p>

scholarly journals Design of Multiple Dependent State Sampling Plan Application for COVID-19 Data Using Exponentiated Weibull Distribution

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Srinivasa Rao Gadde ◽  
Arnold K. Fulment ◽  
Josephat K. Peter
Keyword(s):  
Weibull Distribution ◽  
Operating Characteristic ◽  
Characteristic Curve ◽  
Sampling Plan ◽  
Exponentiated Weibull Distribution ◽  
Exponentiated Weibull ◽  
Single Sampling Plan ◽  
Truncated Life Test ◽  
Dependent State

The proposed sampling plan in this article is referred to as multiple dependent state (MDS) sampling plans, for rejecting a lot based on properties of the current and preceding lot sampled. The median life of the product for the proposed sampling plan is assured based on a time-truncated life test, when a lifetime of the product follows exponentiated Weibull distribution (EWD). For the proposed plan, optimal parameters such as the number of preceding lots required for deciding whether to accept or reject the current lot, sample size, and rejection and acceptance numbers are obtained by the approach of two points on the operating characteristic curve (OC curve). Tables are constructed for various combinations of consumer and producer’s risks for various shape parameters. The proposed MDS sampling plan for EWD is demonstrated using the coronavirus (COVID-19) outbreak in China. The performance of the proposed sampling plan is compared with the existing single-sampling plan (SSP) when the quality of the product follows EWD.

A New-Flexible Generated Family of Distributions Based on Half-Logistic Distribution

2020 ◽  
Vol 17 (11) ◽  
pp. 4813-4818
Author(s):  
Sanaa Al-Marzouki ◽  
Sharifah Alrajhi
Keyword(s):  
Logistic Model ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Data Set ◽  
New Family ◽  
Probability Weighted Moment ◽  
The Subject ◽  
Generated Family ◽  
Family Of Distributions

We proposed a new family of distributions from a half logistic model called the generalized odd half logistic family. We expressed its density function as a linear combination of exponentiated densities. We calculate some statistical properties as the moments, probability weighted moment, quantile and order statistics. Two new special models are mentioned. We study the estimation of the parameters for the odd generalized half logistic exponential and the odd generalized half logistic Rayleigh models by using maximum likelihood method. One real data set is assesed to illustrate the usefulness of the subject family.

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