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Distribution fitting
About: Distribution fitting is a research topic. Over the lifetime, 1741 publications have been published within this topic receiving 35007 citations.
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TL;DR: In this article, the authors introduced a general class of distributions generated from the logit of the beta random variable, a special case of this family is the beta-normal distribution, which provides great flexibility in modeling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions.
Abstract: This paper introduces a general class of distributions generated from the logit of the beta random variable. A special case of this family is the beta-normal distribution. The shape properties of the beta-normal distribution are discussed. Estimation of parameters of the beta-normal distribution by the maximum likelihood method is also discussed. The beta-normal distribution provides great flexibility in modeling not only symmetric heavy-tailed distributions, but also skewed and bimodal distributions. The flexibility of this distribution is illustrated by applying it to two empirical data sets and comparing the results to previously used methods.
1,043 citations
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TL;DR: In this paper, the authors define a class of distribution free measures of goodness of fit; their exact distribution for small samples can be calculated by means of a computer and two of them have the same asymptotic distribution as the Kolmogorov-Smirnov statistic.
Abstract: This Paper defines a class of distribution free measures of goodness of fit; their exact distribution for small samples can be calculated by means of a computer. Two of them have the same asymptotic distribution as the Kolmogorov-Smirnov statistic.
999 citations
TL;DR: In this article, the Weibull function is used for representation of the wind speed frequency distribution and methods for estimating the two Weibbull parameters (scale factor c and shape factor k) from simple wind statistics are presented.
Abstract: The Weibull function is discussed for representation of the wind speed frequency distribution. Methods are presented for estimating the two Weibull parameters (scale factor c and shape factor k) from simple wind statistics. Comparison is made with a recently proposed method based on the “square-root-normal” distribution with mean wind speed and fastest mile data as input statistics. The Weibull distribution is shown to give smaller root-mean-square errors than the square-root-normal distribution when fitting actual distributions of observed wind speed. Another advantage of the Weibull distribution is the available methodology for projecting to another height the observed Weibull distribution parameters at anemometer height.
706 citations
15 Oct 1999
TL;DR: In this paper, a case study of PARAMETER and QUANTILE ESTIMATION is presented, where the authors use moment ratio diagrams (MRDs) to estimate the probability of fit tests.
Abstract: INTRODUCTION Hydrologic Frequency Analysis General Aspects and Approaches Other Models Return Period, Probability, and Plotting Positions Flood Frequency Models Hydrologic Risk Regionalization Tests on Hydrologic Data SELECTION AND EVALUATION OF PARENT DISTRIBUTION: CONVENTIONAL MOMENTS Moments of Distributions and Their Sample Estimates Moment Ratio Diagrams (MRDs) Probability Plots Selection of Distributions Regional Homogeneity and Regionalization SELECTION AND EVALUATION OF PARENT DISTRIBUTIONS: PROBABILITY WEIGHTED MOMENTS AND L-MOMENTS Moments of Distributions and Their Sample Estimates L-Moment Ratio Diagrams Goodness of Fit Tests A Case Study PARAMETER AND QUANTILE ESTIMATION Introduction Parameter Estimation Quantile Estimation Confidence Intervals NORMAL AND RELATED DISTRIBUTIONS Normal Distribution Two-Parameter Lognormal (LN(2)) Distribution Three-Parameter Lognormal (LM(3)) Distribution GAMMA FAMILY Exponential Distribution Two-Parameter Gamma (G(2)) Distribution Pearson (2) Distribution Log-Pearson (3) Distribution U.S. Water Resources Council Method (WRCM) EXTREME VALUE DISTRIBUTIONS Generalized Extreme Value (GEV) Distribution The Extreme Value Type (EV(1) Distribution Weibul Distribution WAKEBY FAMILY The 5-Parameter Wakeby Distribution (WAK(5)) The 4-Parameter Wakeby Distribution (WAK(4)) The Generalized Pareto Distribution LOGISTIC DISTRIBUTIONS Logistic Distribution Generalized Logistic Distribution COMPUTER PROGRAM Introduction Description of Program REFERENCES
657 citations
01 Jan 1957
503 citations