The fitting of lifetime distribution in real-life data has been studied in various fields of research. With the theory of evolution still applicable, more complex data from real-world scenarios will continue to emerge...The fitting of lifetime distribution in real-life data has been studied in various fields of research. With the theory of evolution still applicable, more complex data from real-world scenarios will continue to emerge. Despite this, many researchers have made commendable efforts to develop new lifetime distributions that can fit this complex data. In this paper, we utilized the KM-transformation technique to increase the flexibility of the power Lindley distribution, resulting in the Kavya-Manoharan Power Lindley (KMPL) distribution. We study the mathematical treatments of the KMPL distribution in detail and adapt the widely used method of maximum likelihood to estimate the unknown parameters of the KMPL distribution. We carry out a Monte Carlo simulation study to investigate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the KMPL distribution. To demonstrate the effectiveness of the KMPL distribution for data fitting, we use a real dataset comprising the waiting time of 100 bank customers. We compare the KMPL distribution with other models that are extensions of the power Lindley distribution. Based on some statistical model selection criteria, the summary results of the analysis were in favor of the KMPL distribution. We further investigate the density fit and probability-probability (p-p) plots to validate the superiority of the KMPL distribution over the competing distributions for fitting the waiting time dataset.展开更多
A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Aus...A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.展开更多
In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulati...In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulation process is conducted to evaluate their controlling of type 1 error and their power functions. Generally, the weighted Kolmogrov-Smirnov test statistics show a relatively better performance than both, the Cramer von-Miss and the Anderson Darling test statistics. For large sample values, the Anderson Darling test statistics cannot control type 1 error but for relatively small sample values it indicates a better performance than the Cramer von-Miss test statistics. Best selection of the test statistics and highlights for future studies are also explored.展开更多
SSE(sag state estimation)算法是一种用于电压跌落状态估计的二阶曲线拟合算法,其精度受监测数据精度影响严重,若监测关键点存在不良数据会导致整个配电网电压跌落状态的估计错误。基于此,提出了电压跌落状态估计不良数据检测算法,并...SSE(sag state estimation)算法是一种用于电压跌落状态估计的二阶曲线拟合算法,其精度受监测数据精度影响严重,若监测关键点存在不良数据会导致整个配电网电压跌落状态的估计错误。基于此,提出了电压跌落状态估计不良数据检测算法,并构造了修正不良数据的数学模型。算例结果证明,该算法能够有效识别不良数据,提高电压跌落状态估计精度。展开更多
文摘The fitting of lifetime distribution in real-life data has been studied in various fields of research. With the theory of evolution still applicable, more complex data from real-world scenarios will continue to emerge. Despite this, many researchers have made commendable efforts to develop new lifetime distributions that can fit this complex data. In this paper, we utilized the KM-transformation technique to increase the flexibility of the power Lindley distribution, resulting in the Kavya-Manoharan Power Lindley (KMPL) distribution. We study the mathematical treatments of the KMPL distribution in detail and adapt the widely used method of maximum likelihood to estimate the unknown parameters of the KMPL distribution. We carry out a Monte Carlo simulation study to investigate the performance of the Maximum Likelihood Estimates (MLEs) of the parameters of the KMPL distribution. To demonstrate the effectiveness of the KMPL distribution for data fitting, we use a real dataset comprising the waiting time of 100 bank customers. We compare the KMPL distribution with other models that are extensions of the power Lindley distribution. Based on some statistical model selection criteria, the summary results of the analysis were in favor of the KMPL distribution. We further investigate the density fit and probability-probability (p-p) plots to validate the superiority of the KMPL distribution over the competing distributions for fitting the waiting time dataset.
文摘A method is presented to extrapolate a time series of wave data to extreme wave heights. The 15-year time series of deepwater wave data collected for 34 min every hour from 1988 to 2002 in the South Pacific Ocean, Australia, is analyzed to generate a set of storm peak wave heights by use of the Peaks-Over-Threshold method. The probability distribution is calculated by grouping the observod storm peak wave heights into a number of wave height classes and assigning a probability to each wave height class. The observed probability distribution is then fitted to eight different probability distribution functions and found to be fitted best by the Weibull distribution （a = 1.17）, nearly best by the FT-Ⅰ, quite well by the exponential, and poorly by the lognormal function based on the criterion of the sum of squares of the errors, SSE （H）. The effect of the threshold wave height on the estimated extreme wave height is also studied and is found insignificant in this study. The 95 % prediction intervals of the best-fit FT-Ⅰ , exponential and Weibull functions are also derived.
文摘In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulation process is conducted to evaluate their controlling of type 1 error and their power functions. Generally, the weighted Kolmogrov-Smirnov test statistics show a relatively better performance than both, the Cramer von-Miss and the Anderson Darling test statistics. For large sample values, the Anderson Darling test statistics cannot control type 1 error but for relatively small sample values it indicates a better performance than the Cramer von-Miss test statistics. Best selection of the test statistics and highlights for future studies are also explored.
文摘SSE(sag state estimation)算法是一种用于电压跌落状态估计的二阶曲线拟合算法,其精度受监测数据精度影响严重,若监测关键点存在不良数据会导致整个配电网电压跌落状态的估计错误。基于此,提出了电压跌落状态估计不良数据检测算法,并构造了修正不良数据的数学模型。算例结果证明,该算法能够有效识别不良数据,提高电压跌落状态估计精度。
