The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fittin...The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fitting a given dataset and can provide the initial estimate of the model parameters. The decision on the appropriateness of a distribution is somehow subjective. This paper presents a probability plot of the log-Weibull distribution(LWPP). The distribution of the probability plot correlation coefficient is studied. From this distribution, a lower confidence limit is determined for determining whether the probability plot correlation coefficient derived from a given data set is large enough. The appropriateness and usefulness of this study are illustrated by two real-world examples.展开更多
The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location par...The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.展开更多
Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction ...Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.展开更多
This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q...This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.展开更多
With the rapid development in the field of modern agriculture,an in-depth investigation into various types of agricultural carbon emissions provides essential insights into understanding the spatial patterns and evolv...With the rapid development in the field of modern agriculture,an in-depth investigation into various types of agricultural carbon emissions provides essential insights into understanding the spatial patterns and evolving trends of agricultural carbon emissions in China.Taking Liaoning Province as a case study,this paper collects historical monitoring data on agricultural carbon emissions from all provinces and direct-controlled municipalities in China from 2000 to 2020.The data undergoes preprocessing,with missing values addressed using the nearest-neighbor imputation method.Subsequently,based on the IPCC carbon emission coefficient method,the paper calculates the annual agricultural carbon emissions for various categories in Liaoning Province.The study employs scatter plots to make preliminary judgments on the correlation between different carbon emission categories.Finally,an in-depth analysis is conducted using the Spearman correlation coefficient method to explore the relationships among different carbon sources.The research reveals a high correlation among certain carbon sources,providing scientific guidance for reducing agricultural carbon emissions.展开更多
基金the National Natural Science Foundation of China(No.71371035)
文摘The log-Weibull distribution is a variant of the three-parameter Weibull distribution. The probability plot of a distribution model is desired since it can help to decide on whether the model is appropriate for fitting a given dataset and can provide the initial estimate of the model parameters. The decision on the appropriateness of a distribution is somehow subjective. This paper presents a probability plot of the log-Weibull distribution(LWPP). The distribution of the probability plot correlation coefficient is studied. From this distribution, a lower confidence limit is determined for determining whether the probability plot correlation coefficient derived from a given data set is large enough. The appropriateness and usefulness of this study are illustrated by two real-world examples.
基金National Natural Science Foundation of China(No.71371035)
文摘The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.
基金This research is supported by National Key Research and Development Project(Grant Number 2019YFD0901002)Also Natural Science Foundation of Liaoning Province(Grant Number 20170540105)Liaoning Province Education Foundation(Grant Number JL201913)are gratefully acknowledged.
文摘Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.
文摘This paper investigates the normality of some real data set obtained from waist measurements of a group of 49 young adults. The quantile - quantile （Q-Q） plot and the analysis of correlation coefficients for the Q-Q plot is used to determine the normality or otherwise of the data set. In this regards, the probabilities of the quantiles were computed, modified and plotted. Thereafter the correlation coefficients for the quantile - quantile plots were obtained. Results indicate that at 0.1 level of significance, the data for young adult males of the sample were not normally distributed, and had a mean value that is within the range of low risk, healthwise, whereas the distribution of the data for young female adults showed reasonable normality, but also with a mean value that is within the range of low risk in terms of health condition.
文摘With the rapid development in the field of modern agriculture,an in-depth investigation into various types of agricultural carbon emissions provides essential insights into understanding the spatial patterns and evolving trends of agricultural carbon emissions in China.Taking Liaoning Province as a case study,this paper collects historical monitoring data on agricultural carbon emissions from all provinces and direct-controlled municipalities in China from 2000 to 2020.The data undergoes preprocessing,with missing values addressed using the nearest-neighbor imputation method.Subsequently,based on the IPCC carbon emission coefficient method,the paper calculates the annual agricultural carbon emissions for various categories in Liaoning Province.The study employs scatter plots to make preliminary judgments on the correlation between different carbon emission categories.Finally,an in-depth analysis is conducted using the Spearman correlation coefficient method to explore the relationships among different carbon sources.The research reveals a high correlation among certain carbon sources,providing scientific guidance for reducing agricultural carbon emissions.
