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Krishnamoorthy K, Murshed MM. Confidence estimation based on data from independent studies. Stat Methods Med Res 2024; 33:42-60. [PMID: 38055982 DOI: 10.1177/09622802231217644] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
The problem of finding confidence intervals based on data from several independent studies or experiments is considered. A general method of finding confidence intervals by inverting a combined test is proposed. The combined tests considered are the Fisher test, the weighted inverse normal test, the inverse chi-square test and the inverse Cauchy test. The method is illustrated for finding confidence intervals for a common mean of several normal populations, common correlation coefficient of several bivariate normal populations, common coefficient of variation, common mean of several lognormal populations, and for a common mean of several gamma populations. For each case, the confidence intervals based on the combined tests are compared with the other available approximate confidence intervals with respect to coverage probability and precision. R functions to compute all confidence intervals are provided in a supplementary file. The methods are illustrated using several practical examples.
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Affiliation(s)
| | - Md Monzur Murshed
- Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA
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2
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Confidence Intervals for Common Coefficient of Variation of Several Birnbaum–Saunders Distributions. Symmetry (Basel) 2022. [DOI: 10.3390/sym14102101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
The Birnbaum–Saunders (BS) distribution, also known as the fatigue life distribution, is right-skewed and used to model the failure times of industrial components. It has received much attention due to its attractive properties and its relationship to the normal distribution (which is symmetric). Furthermore, the coefficient of variation (CV) is commonly used to analyze variation within a dataset. In some situations, the independent samples are collected from different instruments or laboratories. Consequently, it is of importance to make inference for the common CV. To this end, confidence intervals based on the generalized confidence interval (GCI), method of variance estimates recovery (MOVER), large-sample (LS), Bayesian credible interval (BayCrI), and highest posterior density interval (HPDI) methods are proposed herein to estimate the common CV of several BS distributions. Their performances in terms of their coverage probabilities and average lengths were investigated by using Monte Carlo simulation. The simulation results indicate that the HPDI-based confidence interval outperformed the others in all of the investigated scenarios. Finally, the efficacies of the proposed confidence intervals are illustrated by applying them to real datasets of PM10 (particulate matter ≤ 10 μm) concentrations from three pollution monitoring stations in Chiang Mai, Thailand.
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3
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Jana N, Gautam M. Interval estimation of the common mean and difference of medians for a bivariate lognormal distribution. J STAT COMPUT SIM 2022. [DOI: 10.1080/00949655.2022.2102632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/16/2022]
Affiliation(s)
- Nabakumar Jana
- Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, India
| | - Meenakshi Gautam
- Department of Mathematics and Computing, Indian Institute of Technology (ISM) Dhanbad, Dhanbad, India
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4
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Yosboonruang N, Niwitpong SA, Niwitpong S. Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand. PeerJ 2022; 10:e12858. [PMID: 35186465 PMCID: PMC8820225 DOI: 10.7717/peerj.12858] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Accepted: 01/09/2022] [Indexed: 01/10/2023] Open
Abstract
Rainfall fluctuation makes precipitation and flood prediction difficult. The coefficient of variation can be used to measure rainfall dispersion to produce information for predicting future rainfall, thereby mitigating future disasters. Rainfall data usually consist of positive and true zero values that correspond to a delta-lognormal distribution. Therefore, the coefficient of variation of delta-lognormal distribution is appropriate to measure the rainfall dispersion more than lognormal distribution. In particular, the measurement of the dispersion of precipitation from several areas can be determined by measuring the common coefficient of variation in the rainfall from those areas together. Herein, we compose confidence intervals for the common coefficient of variation of delta-lognormal distributions by employing the fiducial generalized confidence interval, equal-tailed Bayesian credible intervals incorporating the independent Jeffreys or uniform priors, and the method of variance estimates recovery. A combination of the coverage probabilities and expected lengths of the proposed methods obtained via a Monte Carlo simulation study were used to compare their performances. The results show that the equal-tailed Bayesian based on the independent Jeffreys prior was suitable. In addition, it can be used the equal-tailed Bayesian based on the uniform prior as an alternative. The efficacies of the proposed confidence intervals are demonstrated via applying them to analyze daily rainfall datasets from Nan, Thailand.
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Malekzadeh A, Sabri-Laghaie K. Quantile-based reliability comparison of products: Applied to Log-normal distribution. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2019.1600706] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Ahad Malekzadeh
- Department of Computer Science and Statistics, Faculty of Mathematics, K.N. Toosi University of Technology, Tehran, Iran
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6
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Maneerat P, Niwitpong SA. Estimating the average daily rainfall in Thailand using confidence intervals for the common mean of several delta-lognormal distributions. PeerJ 2021; 9:e10758. [PMID: 33552739 PMCID: PMC7831370 DOI: 10.7717/peerj.10758] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 12/21/2020] [Indexed: 11/20/2022] Open
Abstract
The daily average natural rainfall amounts in the five regions of Thailand can be estimated using the confidence intervals for the common mean of several delta-lognormal distributions based on the fiducial generalized confidence interval (FGCI), large sample (LS), method of variance estimates recovery (MOVER), parametric bootstrap (PB), and highest posterior density intervals based on Jeffreys' rule (HPD-JR) and normal-gamma-beta (HPD-NGB) priors. Monte Carlo simulation was conducted to assess the performance in terms of the coverage probability and average length of the proposed methods. The numerical results indicate that MOVER and PB provided better performances than the other methods in a variety of situations, even when the sample case was large. The efficacies of the proposed methods were illustrated by applying them to real rainfall datasets from the five regions of Thailand.
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Affiliation(s)
- Patcharee Maneerat
- Department of Mathematics, Faculty of Science and Technology, Uttaradit Rajabhat University, Uttaradit, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
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7
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Comparing scale parameters in several gamma distributions with known shapes. Comput Stat 2020. [DOI: 10.1007/s00180-020-00983-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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8
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Thangjai W, Niwitpong SA, Niwitpong S. Confidence intervals for the common coefficient of variation of rainfall in Thailand. PeerJ 2020; 8:e10004. [PMID: 33005493 PMCID: PMC7513754 DOI: 10.7717/peerj.10004] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Accepted: 08/30/2020] [Indexed: 11/20/2022] Open
Abstract
The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (n I < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.
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Affiliation(s)
- Warisa Thangjai
- Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangok, Bangkok, Thailand
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9
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Maneerat P, Niwitpong SA. Comparing Medical Care Costs using Bayesian Credible Intervals for the Ratio of Means of Delta-Lognormal Distributions. INT J UNCERTAIN FUZZ 2020. [DOI: 10.1142/s021848852040005x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
When considering the medical care costs data with a high proportion of zero items of two inpatient groups, comparing them can be estimated using confidence intervals for the ratio of the means of two delta-lognormal distributions. The Bayesian credible interval-based uniform-beta prior (BCIh-UB) is proposed and compared with the generalized confidence interval (GCI), fiducial GCI (FGCI), the method of variance estimates recovery (MOVER), BCIh based on Jeffreys’ rule prior (BCIh-JR), and BCIh based on the normal-gamma prior (BCIh-NG). The coverage probability (CP), average length (AL), and lower and upper error rates were the performance measures applied for assessing the methods through a Monte Carlo simulation. A numerical evaluation showed that BCIh-UB had much better CP and AL than the others even with a large difference between the variances and with a high proportion of zero. Finally, to illustrate the efficacy of BCIh-UB, the methods were applied to two sets of medical care costs data.
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Affiliation(s)
- Patcharee Maneerat
- Department of Mathematics, Uttaradit Rajabhat University, Uttaradit 53000, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
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10
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Gökpınar E. Standardized likelihood ratio test for homogeneity of variance of several normal populations. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1800037] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Esra Gökpınar
- Department of Statistics, Gazi University, Ankara, Turkey
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Maneerat P, Niwitpong SA, Niwitpong S. A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand. PeerJ 2020; 8:e8502. [PMID: 32095346 PMCID: PMC7020819 DOI: 10.7717/peerj.8502] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2019] [Accepted: 01/01/2020] [Indexed: 11/20/2022] Open
Abstract
Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.
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Affiliation(s)
- Patcharee Maneerat
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, Thailand
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12
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Cakmak M, Gokpinar E, Gokpinar F, Ebegil M. A revisit to testing the equality of means for several lognormal distributions. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1713131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Mehmet Cakmak
- The Scientific and Technological Research Council of Turkey, Ankara, Turkey
| | - Esra Gokpinar
- Department of Statistics, Gazi University, Ankara, Turkey
| | - Fikri Gokpinar
- Department of Statistics, Gazi University, Ankara, Turkey
| | - Meral Ebegil
- Department of Statistics, Gazi University, Ankara, Turkey
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13
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Gökpınar E. Standardized Log-Likelihood Ratio Test for the Equality of Inverse Gaussian Scale Parameters. IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY, TRANSACTIONS A: SCIENCE 2019. [DOI: 10.1007/s40995-018-0617-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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14
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Maneerat P, Niwitpong SA, Niwitpong S. Bayesian confidence intervals for a single mean and the difference between two means of delta-lognormal distributions. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1616095] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Patcharee Maneerat
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
| | - Sa-Aat Niwitpong
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
| | - Suparat Niwitpong
- Department of Applied Statistics, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
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15
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Malekzadeh A, Kharrati-Kopaei M. Inferences on the common mean of several heterogeneous log-normal distributions. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1531980] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Ahad Malekzadeh
- Department of Mathematics, K.N. Toosi University of Technology, Tehran, Iran
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