Estimating average wind speed in Thailand using confidence intervals for common mean of several Weibull distributions

PeerJ

article

Manussaya La-ongkaew¹  Sa-Aat Niwitpong¹  Suparat Niwitpong¹ 

[1] Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok

关键词: Common mean;    Bayesian method;    Prior gamma distribution;    Equitailed confidence interval;    The highest posterior density;    Generalized confidence interval;    Adjusted method of variance estimates recovery;    Simulation;   

DOI  :  10.7717/peerj.15513

学科分类：社会科学、人文和艺术（综合）

来源: Inra

【 摘 要 】

The Weibull distribution has been used to analyze data from many fields, including engineering, survival and lifetime analysis, and weather forecasting, particularly wind speed data. It is useful to measure the central tendency of wind speed data in specific locations using statistical parameters for instance the mean to accurately forecast the severity of future catastrophic events. In particular, the common mean of several independent wind speed samples collected from different locations is a useful statistic. To explore wind speed data from several areas in Surat Thani province, a large province in southern Thailand, we constructed estimates of the confidence interval for the common mean of several Weibull distributions using the Bayesian equitailed confidence interval and the highest posterior density interval using the gamma prior. Their performances are compared with those of the generalized confidence interval and the adjusted method of variance estimates recovery based on their coverage probabilities and expected lengths. The results demonstrate that when the common mean is small and the sample size is large, the Bayesian highest posterior density interval performed the best since its coverage probabilities were higher than the nominal confidence level and it provided the shortest expected lengths. Moreover, the generalized confidence interval performed well in some scenarios whereas adjusted method of variance estimates recovery did not. The approaches were used to estimate the common mean of real wind speed datasets from several areas in Surat Thani province, Thailand, fitted to Weibull distributions. These results support the simulation results in that the Bayesian methods performed the best. Hence, the Bayesian highest posterior density interval is the most appropriate method for establishing the confidence interval for the common mean of several Weibull distributions.

【 授权许可】

CC BY