Bayesian interval estimations for the mean of delta-three parameter lognormal distribution with application to heavy rainfall data

Maneerat, Patcharee; Nakjai, Pisit; Niwitpong, Sa-Aat

doi:10.1371/journal.pone.0266455

Cited by 3 publications

(1 citation statement)

References 29 publications

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“… Thangjai, Niwitpong & Niwitpong (2020) applied Bayesian methodology to construct estimates of the confidence interval for the mean of a normal distribution with an unknown coefficient of variation. Maneerat, Nakjai & Niwitpong (2022) proposed using Bayesian noninformative priors to estimate the confidence interval for the mean of a three-parameter delta-lognormal distribution. Moreover, functions of the mean such as the difference between and the ratio of two means have also been reported.…”

Section: Introductionmentioning

confidence: 99%

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

La-ongkaew

Niwitpong

2023

PeerJ

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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.

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Section: Introductionmentioning

confidence: 99%

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

La-ongkaew

Niwitpong

2023

PeerJ

Self Cite

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A Modified Stochastic Model for Rainfall Prediction Using Fuzzy Aquila Optimization

Singh

2023

Int. J. Comp. Intel. Appl.

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In recent years, rainfall prediction has received major attention in research areas because of its demanding applications in pollution control management and flood control management. Despite having numerous learning-based approaches to calculate future rainfall trends, it remains inefficient to predict rainfall occurrences by learning linear and nonlinear data patterns of historical weather information (i.e., exact prediction value is complicated to be predicted). These complications are addressed with the evolution of stochastic models which have a greater ability to minimize prediction bias and represent long-term weather variability. Therefore, this paper proposes a novel modified stochastic fuzzy Aquila (MSFA) algorithm to make precise predictions regarding future trends by evaluating rainfall time series data. The proposed MSFA algorithm is applied in rainfall prediction applications in evaluating the effectiveness of the proposed stochastic model. Here, 10 features of the open weather dataset collected from Tamil Nadu are provided as input for the proposed rainfall prediction design. The data inconsistencies such as undesirable format and missing values are structured using preprocessing procedures, namely data arrangement, null value removal, and data partitioning. The preprocessed data are fed into the proposed MSFA algorithm which learns the data features more precisely and predicts the probable occurrence of rainfall. To evaluate the performances of the proposed MSFA algorithm, the metrics such as mean absolute error (MAE), coefficient of determination, root mean squared logarithmic error (RMSLE), and root mean square error (RMSE) are analyzed. The experimental results illustrate that the proposed MSFA algorithm achieves superior performance in terms of all metrics.

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Estimation methods for the ratio of medians of three-parameter lognormal distributions containing zero values and their application to wind speed data from northern Thailand

Maneerat

Nakjai

Niwitpong

2022

PeerJ

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Wind speed has an important impact on the formation and dispersion of fine particulate matter (PM), which can cause several health problems. During the transition from the winter to the summer season in northern Thailand, the wind speed has been low for longer than usual, which has resulted in fine PM accumulating in the air. Motivated by this, we have identified a need to investigate wind speed due to its effect on PM formation and dispersion and to raise awareness among the general public. The hourly windspeed can be approximated by using confidence intervals for the ratio of the medians of three-parameter lognormal distributions containing zero values. Thus, we constructed them by using fiducial, normal approximation, and Bayesian methods. By way of comparison, the performance measures for all ofthe proposed methods (the coverage percentage, lower and upper error probabilities (LEP and UEP,respectively), and expected length) were assessed via Monte Carlo simulation. The results of Monte Carlo simulation studies show that the Bayesian method provided coverage percentages close to the nominal confidence level and shorter intervals than the other methods. Importantly, it maintained a good balance between LEP and UEP even for large variation and percentage of zero-valued observations. To illustrate the efficacy of our proposed methods, we applied them to hourly wind speed data from northern Thailand.

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Bayesian interval estimations for the mean of delta-three parameter lognormal distribution with application to heavy rainfall data

Cited by 3 publications

References 29 publications

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

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

A Modified Stochastic Model for Rainfall Prediction Using Fuzzy Aquila Optimization

Estimation methods for the ratio of medians of three-parameter lognormal distributions containing zero values and their application to wind speed data from northern Thailand

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