Maximum likelihood estimation of the four-parameter Kappa distribution using the penalty method

Park, Jeong‐Soo; Park, Byung Jun

doi:10.1016/s0098-3004(01)00069-3

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…Winchester [17] compared the performance of MLE and L-Moments in this distribution. Park and Park [19] presented the method of Maximum Likelihood to estimate the parameters of K4D, while Park and Yoon Kim [20] investigated the Fisher information matrix for K4D. Moreover, Park et al [21] studied a three-parameter Kappa distribution, including the comparison of MLE and L-Moment estimates.…”

Section: -Four Parameter Kappa Distributionmentioning

confidence: 99%

The Partial L-Moment of the Four Kappa Distribution

Guayjarernpanishk,

Bussababodhin,

Chiangpradit

2023

Emerg Sci J

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Statistical analysis of extreme events such as flood events is often carried out to predict large return period events. The behaviour of extreme events not only involves heavy-tailed distributions but also skewed distributions, similar to the four-parameter Kappa distribution (K4D). In general, this covers many extreme distributions such as the generalized logistic distribution (GLD), the generalized extreme value distribution (GEV), the generalized Pareto distribution (GPD), and so on. To utilize these distributions, we have to estimate parameters accurately. There are many parameter estimation methods, for example, Method of Moments, Maximum Likelihood Estimator, L-Moments, or partial L-Moments. Nowadays, no researchers have applied the partial L-Moments method to estimate the parameters of K4D. Therefore, the objective of this paper is to derive the partial L-Moments (PL-Moments) for K4D, namely the PL-Moments of the K4D in order to estimate hydrological extremes from censored data. The findings of this paper are formulas of parameter estimation for K4D based on the PL-Moments approach. We have derived the Partial Probability-Weighted Moments (PPWMs) of the K4D (β'r) and derive the estimation of parameters when separated by shape parameters (k,h) conditions i.e., case k>-1 and h>0, case k>-1 and h=0 and case -1<k<-1/h and h<0. Finally, we expect that the parameter estimate for K4D from this formula will help to make accurate forecasts. Doi: 10.28991/ESJ-2023-07-04-06 Full Text: PDF

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Section: -Four Parameter Kappa Distributionmentioning

confidence: 99%

The Partial L-Moment of the Four Kappa Distribution

Guayjarernpanishk,

Bussababodhin,

Chiangpradit

2023

Emerg Sci J

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“…Since no explicit minimizer is possible, a quasi-Newton algorithm is implemented using the "optim" function in the R program [24] to minimize Equation (4). Park and Park [25] calculated the MLE of the K4D parameters employing a penalty method.…”

Section: Maximum Likelihood Estimationmentioning

confidence: 99%

Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution

2020

Self Cite

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Maximum likelihood estimation (MLE) of the four-parameter kappa distribution (K4D) is known to be occasionally unstable for small sample sizes and to be very sensitive to outliers. To overcome this problem, this study proposes Bayesian analysis of the K4D. Bayesian estimators are obtained by virtue of a posterior distribution using the random walk Metropolis–Hastings algorithm. Five different priors are considered. The properties of the Bayesian estimators are verified in a simulation study. The empirical Bayesian method turns out to work well. Our approach is then compared to the MLE and the method of the L-moments estimator by calculating the 20-year return level, the confidence interval, and various goodness-of-fit measures. It is also compared to modeling using the generalized extreme value distribution. We illustrate the usefulness of our approach in an application to the annual maximum wind speeds in Udon Thani, Thailand, and to the annual maximum sea-levels in Fremantle, Australia. In the latter example, non-stationarity is modeled through a trend in time on the location parameter. We conclude that Bayesian inference for K4D may be substantially useful for modeling extreme events.

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“…Analogously to the conventional moments, the LMOM of order one to four characterize location, scale, skewness and kurtosis, respectively. The main advantages of using the method of LMOM are that the parameter estimates are more reliable (i.e., smaller mean-squared error of estimation) and are more robust against outliers than MOM and are usually computationally more tractable than ML (maximum likelihood) method [4] . The LMOM have found wide applications in such fields of applied research as civil engineering, meteorology and hydrology.…”

Section: Introductionmentioning

confidence: 99%

LQ-Moments: Application to the Log-Normal distribution

Shabri¹,

Jemain²

2006

J. of Mathematics and Statistics

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Mudolkar and Hutson (1998) extended L-moments to new moment like entitles called LQmoments (LQMOM). The LQMOM are constructed by using functional defining the quick estimators, where the parameters of quick estimator take the values p = 0, α = 1 for the median, p = 1/4, α = 1/4 for the trimean and p = 0.3, α = 1/3 for the Gastwirth, in places of expectations in L-moments (LMOM). The objective of this paper is to develop improved LQMOM that do not impose restrictions on the value of p and α such as the median, trimean or the Gastwirth but we explore an extended class of LQMOM with consideration combinations of p and α values in the range 0 and 0.5. The popular quantile estimator namely the weighted kernel quantile (WKQ) estimator will be proposed to estimate the quantile function. Monte Carlo simulations are conducted to illustrate the performance of the proposed estimators of the log-normal 3 (LN3) distribution were compared with the estimators based on conventional LMOM and MOM (method of moments) for various sample sizes and return periods

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Maximum likelihood estimation of the four-parameter Kappa distribution using the penalty method

Cited by 7 publications

References 4 publications

The Partial L-Moment of the Four Kappa Distribution

The Partial L-Moment of the Four Kappa Distribution

Bayesian Inference in Extremes Using the Four-Parameter Kappa Distribution

LQ-Moments: Application to the Log-Normal distribution

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