This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha p...This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.展开更多
The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of...The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.展开更多
In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confiden...In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.展开更多
Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibili...Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.展开更多
This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters an...This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.展开更多
An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model i...An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model is adopted in this study to describe the thermal decomposition mechanism.The Weibull distribution function is used to record and analyze the weight loss during isothermal decomposition at different temperatures(500,600,700,and 800°C).The total weight loss of the pine sawdust is assumed as a linear combination of individual weight loss from three components,including the char and two volatile matters.The plot of the thermal decomposition rate curve leads to kinetic parameters such as the reaction rate constants and the reaction order.The results show that the Weibull distribution function successfully represents decomposition curves of three components,and fits the experimental data very well.Therefore,this study provides a simple way to evaluate the decomposition rate of biomass combustion in a real combustor.展开更多
Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the cou...Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.展开更多
This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea.The parameter recovery techni...This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea.The parameter recovery technique was used to estimate the three parameters of the Weibull model.The analysis demonstrated satisfactory results based on the following test statistics for the principal percentile models:fit index(FI) range from 0.501(minimum diameter) to 0.932(50th diameter percentiles) and root mean square error(RMSE) range from 0.112(quadratic mean diameter) to 3.572(minimum diameter).The developed model was further evaluated by determining the mean bias(ē) in trees per ha(TPH) for each diameter class,and the results showed highest over-prediction in the 20 cm,andunder-prediction in the 16 cm and 24 cm diameter classes.The goodness of fit tested by KolmogorovSmirnov(KS) test showed no significant differences(p>0.05) between the observed and predicted diameter distributions for almost all plots.Using site index and aboveground biomass(AGB) models developed for P.thunbergii in South Korea,a model to predict the AGB per ha for each diameter class and subsequently the total AGB of the stand was created.An application guide was also created,which will serve as a decision-support tool for forest managers in quantifying the future total AGB in P.thunbergii stands located in the eastern coast of South Korea and,subsequently,the quantification of potential carbon stocks aside from being a vital input in designing efficient management and protection strategies for these stands.展开更多
In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are ...In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.展开更多
In order to improve the accuracy and efficiency of graphical method and maximum likelihood estimation( MLE) in Mixed Weibull distribution parameters estimation,Graphical-GA combines the advantage of graphical method a...In order to improve the accuracy and efficiency of graphical method and maximum likelihood estimation( MLE) in Mixed Weibull distribution parameters estimation,Graphical-GA combines the advantage of graphical method and genetic algorithm( GA) is proposed.Firstly,with the analysis of Weibull probability paper( WPP),mixed Weibull is identified to data fitting.Secondly,the observed value of shape and scale parameters are obtained by graphical method with least square,then optimizing the parameters of mixed Weibull with GA.Thirdly,with the comparative analysis on graphical method,piecewise Weibull and two-Weibull,it shows graphical-GA mixed Weibull is the best.Finally,the spindle MTBF point estimation and interval estimation are got based on mixed Weibull distribution.The results indicate that graphical-GA are improved effectively and the evaluation of spindle can provide the basis for design and reliability growth.展开更多
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No.(PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘This paper suggests a new modified version of the traditional Weibull distribution by adding a new shape parameter utilising the modified alpha power transformed technique.We refer to the new model as modified alpha power transformed Weibull distribution.The attractiveness and significance of the new distribution lie in its power to model monotone and non-monotone failure rate functions,which are quite familiar in environmental investigations.Its hazard rate function can be decreasing,increasing,bathtub and upside-down then bathtub shaped.Diverse structural properties of the proposed model are acquired including quantile function,moments,entropies,order statistics,residual life and reversed failure rate function.The parameters of the distribution were estimated using the maximum likelihood function.The maximum likelihood method is employed to estimate the model parameters and the approximate confidence intervals are also computed.Via a simulation study,the performance of the point and interval estimates are compared using different criteria.Employing real lifetime data sets,we verify that the offered model furnishes a better fit than some other lifetime models including Weibull,gamma and alpha powerWeibull models.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.
基金Supported by the National Natural Science Foundation of China(12171335,12301603)the Science Development Project of Sichuan University(2020SCUNL201)the Scientific Foundation of Nanjing University of Posts and Telecommunications(NY221026)。
文摘In this paper, we consider the construction of the approximate profile-</span><span style="font-family:""> </span><span style="font-family:Verdana;">likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution</span><span style="font-family:""> </span><span style="font-family:Verdana;">under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.
文摘Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.
文摘This study considers the estimation of Maximum Likelihood Estimator and the Bayesian Estimator of the Weibull distribution with interval-censored data. The Bayesian estimation can’t be used to solve the parameters analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the scale and shape parameters are obtained via Metropolis-Hastings algorithm. Also Lindley’s approximation is used. The two methods are compared to maximum likelihood counterparts and the comparisons are made with respect to the mean square error (MSE) to determine the best for estimating of the scale and shape parameters.
基金Supported by the Chung Yuan Christian University (CYCU-97-CR-CE)
文摘An isothermal operation is implemented by employing a thermogravimetric analyzer (TGA) for simulating the thermal decomposition behavior of 58μm pine sawdust in air atmosphere.An independent parallel reaction model is adopted in this study to describe the thermal decomposition mechanism.The Weibull distribution function is used to record and analyze the weight loss during isothermal decomposition at different temperatures(500,600,700,and 800°C).The total weight loss of the pine sawdust is assumed as a linear combination of individual weight loss from three components,including the char and two volatile matters.The plot of the thermal decomposition rate curve leads to kinetic parameters such as the reaction rate constants and the reaction order.The results show that the Weibull distribution function successfully represents decomposition curves of three components,and fits the experimental data very well.Therefore,this study provides a simple way to evaluate the decomposition rate of biomass combustion in a real combustor.
文摘Given the steady increase in use of alternative energy sources to supply part of the energy demand of the world, and considering that Mexico has enough wind resources to produce all the electricity required by the country, in this work, it is carried out the development of a system of wind resource assessment to determine the volume of water that a windmill pumping system can provide in a specific area. To this end, it has developed a computer program for wind resource assessment by measurements of wind speed, direction, temperature, barometric pressure and relative humidity. Measuring equipments were mounted in a wind measurement tower of 10 m high, within the premises of the University of Quintana Roo which is located along the coast. Until this day, there are records over a period of five months of the variables of wind speed, wind direction, temperature, relative humidity and atmospheric pressure. These variables were used for statistical calculations using the Weibull distributions. To give a better use of the calculated data, they were applied to the evaluation of a Pumping System.
基金support from the Forest Science and Technology Projects(Project No.S211415L010140)provided by the Korea Forest Service
文摘This study was carried out to determine the performance of percentile-based Weibull diameter distribution model for Pinus thunbergii stands thriving along the eastern coast of South Korea.The parameter recovery technique was used to estimate the three parameters of the Weibull model.The analysis demonstrated satisfactory results based on the following test statistics for the principal percentile models:fit index(FI) range from 0.501(minimum diameter) to 0.932(50th diameter percentiles) and root mean square error(RMSE) range from 0.112(quadratic mean diameter) to 3.572(minimum diameter).The developed model was further evaluated by determining the mean bias(ē) in trees per ha(TPH) for each diameter class,and the results showed highest over-prediction in the 20 cm,andunder-prediction in the 16 cm and 24 cm diameter classes.The goodness of fit tested by KolmogorovSmirnov(KS) test showed no significant differences(p>0.05) between the observed and predicted diameter distributions for almost all plots.Using site index and aboveground biomass(AGB) models developed for P.thunbergii in South Korea,a model to predict the AGB per ha for each diameter class and subsequently the total AGB of the stand was created.An application guide was also created,which will serve as a decision-support tool for forest managers in quantifying the future total AGB in P.thunbergii stands located in the eastern coast of South Korea and,subsequently,the quantification of potential carbon stocks aside from being a vital input in designing efficient management and protection strategies for these stands.
文摘In this paper, a new probability distribution is proposed by using Marshall and Olkin transformation. Some of its properties such as moments, moment generating function, order statistics and reliability functions are derived. The method of </span><span style="font-family:Verdana;">maximum likelihood is used to estimate the model parameters. The graphs of the reliability function and hazard rate function are plotted by taken some values of the parameters. Three real life applications are introduced to compare the behaviour of the new distribution with other distributions.
基金Sponsored by the Scientific and Technological Developing Project of Jilin Province(Grant No.20140520126JH)the Spring Plan of Ministry of Education(Grant No.Z2014140)+1 种基金the National Natural Science Foundation of China(Grant No.51275205)the Department of Education of Jilin Province(Grant No.2015-80)
文摘In order to improve the accuracy and efficiency of graphical method and maximum likelihood estimation( MLE) in Mixed Weibull distribution parameters estimation,Graphical-GA combines the advantage of graphical method and genetic algorithm( GA) is proposed.Firstly,with the analysis of Weibull probability paper( WPP),mixed Weibull is identified to data fitting.Secondly,the observed value of shape and scale parameters are obtained by graphical method with least square,then optimizing the parameters of mixed Weibull with GA.Thirdly,with the comparative analysis on graphical method,piecewise Weibull and two-Weibull,it shows graphical-GA mixed Weibull is the best.Finally,the spindle MTBF point estimation and interval estimation are got based on mixed Weibull distribution.The results indicate that graphical-GA are improved effectively and the evaluation of spindle can provide the basis for design and reliability growth.