• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.493-505
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• 2017

Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• Journal of Environmental Science International
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• v.26 no.11
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• pp.1247-1253
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• 2017

The Fuji variety of apple, introduced in Japan, has excellent storage quality and good taste, such that it is the most commonly cultivated apple variety in Gunwi County, North Gyeongsang Province, Korean Peninsula. Accurate prediction of harvest maturity allows farmers to more efficiently manage their farm in important aspects such as working time, fruit storage, market shipment, and labor distribution. Temperature is one of the most important factors that determine plant growth, development, and yield. This paper reports on the beta distribution (function) model that can be used to simulate the the phenological response of plants to temperature. The beta function, commonly used as a skewed probability density in statistics, was introduced to estimate apple harvest maturity as a function of temperature in this study. The model parameters were daily maximum temperature, daily optimum temperature, and maximum growth rate. They were estimated from the input data of daily maximum and minimum temperature and apple harvest maturity. The difference in observed and predicted maturity day from 2009 to 2012, with optimal parameters, was from two days earlier to one day later.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.379-389
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• 2002

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.243-255
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• 1996

The number of neutron signals from a neutral particle beam(NPB) at the detector, without any errors, obeys Poisson distribution, Under two assumptions that NPB scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of signals becomes a Poisson-power function distribution. In this paper, we show that the error rate in simple hypothesis testing for the limiting Poisson-power function distribution is not zero. That is, the limit of ${\alpha}+{\beta}$ is zero when Poisson parameter$\kappa\rightarro\infty$, but this limit is not zero (i.e., $\rho\ell$>0)for the Poisson-power function distribution. We also give optimal decision algorithms for a specified error rate.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.81-86
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• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• Horticultural Science & Technology
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• v.34 no.2
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• pp.236-241
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• 2016

The common ice plant (Mesembryanthemum crystallinum L.) has some medicinal uses and recommended plant in closed-type plant factory. The objective of this study was to estimate the cardinal temperatures for seed germination of the common ice plant using bilinear, parabolic, and beta distribution models. Seeds of the common ice plant were germinated in the dark in a growth chamber at four constant temperatures: 16, 20, 24, and $28^{\circ}C$. For this, four replicates of 100 seeds were placed on two layers of filter paper in a 9-cm petri dish and radicle emergence of 0.1 mm was scored as germination. The times to 50% germination were 4.3, 2.5, 2.0, and 1.8 days at 16, 20, 24, and $28^{\circ}C$, respectively, indicating that the germination of this warm-weather crop increased with temperature. Next, the time course of germination was modeled using a logistic function. For the selection of an accurate model, seeds were germinated in the dark at constant temperatures of 6, 12, 32, and $36^{\circ}C$. Germination started earlier and increased rapidly at temperatures above $20^{\circ}C$. The minimum, optimal, and maximum temperatures were estimated by regression of the inverse of time to 50% germination rate, as a function of the temperature gradient. The different functions estimated differing minimum, optimal and maximum temperatures, with 5.7, 27.7, and $36.5^{\circ}C$, respectively for the bilinear function, 13.4, 25.0, and $36.6^{\circ}C$, respectively, for the parabolic function and 7.8, 25.9, and $36.0^{\circ}C$, respectively, for the beta distribution function. The models estimated that the inverse of time to 50% germination rate was 0 at 6 and $36^{\circ}C$. The observed final germination rates at 12 and $32^{\circ}C$ were 62 and 97%, respectively. Our data show that a beta distribution function provides a useful model for estimating the cardinal temperatures for germination of seed from the common ice plant.