• Title, Summary, Keyword: weighted distribution

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Distribution of a Sum of Weighted Noncentral Chi-Square Variables

  • Heo, Sun-Yeong;Chang, Duk-Joon
    • Communications for Statistical Applications and Methods
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    • v.13 no.2
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    • pp.429-440
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    • 2006
  • In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

Families of Distributions Arising from Distributions of Ordered Data

  • Ahmadi, Mosayeb;Razmkhah, M.;Mohtashami Borzadaran, G.R.
    • Communications for Statistical Applications and Methods
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    • v.22 no.2
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    • pp.105-120
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    • 2015
  • A large family of distributions arising from distributions of ordered data is proposed which contains other models studied in the literature. This extension subsume many cases of weighted random variables such as order statistics, records, k-records and many others in variety. Such a distribution can be used for modeling data which are not identical in distribution. Some properties of the theoretical model such as moment, mean deviation, entropy criteria, symmetry and unimodality are derived. The proposed model also studies the problem of parameter estimation and derives maximum likelihood estimators in a weighted gamma distribution. Finally, it will be shown that the proposed model is the best among the previously introduced distributions for modeling a real data set.

An Analysis Regarding Trends of Dualism in Korean Agriculture (농업생산 양극화 추이에 대한 연구)

  • Sung, Jae-Hoon;Woo, Sung-Hwi
    • The Journal of Industrial Distribution & Business
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    • v.8 no.6
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    • pp.87-95
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    • 2017
  • Purpose - The structural changes of Korean agriculture are complex due to heterogeneous production processes and farms' features. This study analyzed trends of dualism in Korean agriculture over the period 2000-15 based on farm-level data to clarify the specific trends of dualism in terms of farm income, farm-size, and farm operators' age. From the results of this study, we would be able to understand the features of structural changes in Korean agriculture more profoundly. Research design, data, and methodology - We incorporated farm-level data in South Korea: Agricultural census and Farm household economy survey. As measures of inequality, we used size-weighted quantiles, and normalized Gini coefficients as well as mean and conventional quantiles. The size-weighted quantiles are more robust to changes in the number of small farms, but they are more sensitive to changes in the distribution of farm-size. Thus, they would be more useful to identify trends of dualism of Korean agriculture. Results - The results show that the farmland distribution of crop farms became more skewed and dispersed. However, the herd distribution of livestock farms became more concentrated. To be specific, their mean and 1st quantile increases more rapidly than their size-weighted 2nd quantile and size-weighted 3rd quantile. Gini coefficients of livestock farms regarding their herd distribution decreased by 0.1 on average. In the case of income distribution, the results indicate that the polarization regarding farm household/agricultural/non-agricultural income became more severe. However, we also found that the distribution of transfer income became concentrated continuously. The results imply that transfer income including subsidies would decrease farm income polarization. Lastly, during the study periods, Korean farms were aging over time, and age distribution of them more concentrated. Conclusions - The structure of Korean agriculture has been changing, even though the absolute size of it decreased over time. Land (herd) distribution became more dispersed (concentrated). Inequality regarding agricultural income became more severe, and it made farm household income more polarized even though transfer income would decrease income gaps among farms. Lastly, farms continue to age regardless of farm types and this might affect the structural changes in Korean agriculture in the future.

A COMPARATIVE EVALUATION OF THE ESTIMATORS OF THE 2-PARAMETER GENERALIZED PARETO DISTRIBUTION

  • Singh, V.P.;Ahmad, M.;Sherif, M.M.
    • Water Engineering Research
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    • v.4 no.3
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    • pp.155-173
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    • 2003
  • Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

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Estimation for scale parameter of type-I extreme value distribution

  • Choi, Byungjin
    • Journal of the Korean Data and Information Science Society
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    • v.26 no.2
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    • pp.535-545
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    • 2015
  • In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

STRONG LAWS FOR WEIGHTED SUMS OF I.I.D. RANDOM VARIABLES

  • Cai, Guang-Hui
    • Communications of the Korean Mathematical Society
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    • v.21 no.4
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    • pp.771-778
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    • 2006
  • Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ([12]).

Potential Impact of Climate Change on Distribution of Hedera rhombea in the Korean Peninsula (기후변화에 따른 송악의 잠재서식지 분포 변화 예측)

  • Park, Seon Uk;Koo, Kyung Ah;Seo, Changwan;Kong, Woo-Seok
    • Journal of Climate Change Research
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    • v.7 no.3
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    • pp.325-334
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    • 2016
  • We projected the distribution of Hedera rhombea, an evergreen broad-leaved climbing plant, under current climate conditions and predicted its future distributions under global warming. Inaddition, weexplained model uncertainty by employing 9 single Species Distribution model (SDM)s to model the distribution of Hedera rhombea. 9 single SDMs were constructed with 736 presence/absence data and 3 temperature and 3 precipitation data. Uncertainty of each SDM was assessed with TSS (Ture Skill Statistics) and AUC (the Area under the curve) value of ROC (receiver operating characteristic) analyses. To reduce model uncertainty, we combined 9 single SDMs weighted by TSS and resulted in an ensemble forecast, a TSS weighted ensemble. We predicted future distributions of Hedera rhombea under future climate conditions for the period of 2050 (2040~2060), which were estimated with HadGEM2-AO. RF (Random Forest), GBM (Generalized Boosted Model) and TSS weighted ensemble model showed higher prediction accuracies (AUC > 0.95, TSS > 0.80) than other SDMs. Based on the projections of TSS weighted ensemble, potential habitats under current climate conditions showed a discrepancy with actual habitats, especially in the northern distribution limit. The observed northern boundary of Hedera rhombea is Ulsan in the eastern Korean Peninsula, but the projected limit was eastern coast of Gangwon province. Geomorphological conditions and the dispersal limitations mediated by birds, the lack of bird habitats at eastern coast of Gangwon Province, account for such discrepancy. In general, potential habitats of Hedera rhombea expanded under future climate conditions, but the extent of expansions depend on RCP scenarios. Potential Habitat of Hedera rhombea expanded into Jeolla-inland area under RCP 4.5, and into Chungnam and Wonsan under RCP 8.5. Our results would be fundamental information for understanding the potential effects of climate change on the distribution of Hedera rhombea.

Generalized Weighted Linear Models Based on Distribution Functions

  • Yeo, In-Kwon
    • Proceedings of the Korean Statistical Society Conference
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    • pp.161-166
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    • 2003
  • In this paper, a new form of generalized linear models is proposed. The proposed models consist of a distribution function of the mean response and a weighted linear combination of distribution functions of covariates. This form addresses a structural problem of the link function in the generalized linear models. Markov chain Monte Carlo methods are used to estimate the parameters within a Bayesian framework.

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ESTIMATION OF SCALE PARAMETER AND P(Y < X) FROM RAYLEIGH DISTRIBUTION

  • Kim, Chan-Soo;Chung, Youn-Shik
    • Journal of the Korean Statistical Society
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    • v.32 no.3
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    • pp.289-298
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    • 2003
  • We consider the estimation problem for the scale parameter of the Rayleigh distribution using weighted balanced loss function (WBLF) which reflects both goodness of fit and precision. Under WBLF, we obtain the optimal estimator which creates a kind of balance between Bayesian and non-Bayesian estimation. We also deal with the estimation of R = P(Y < X) when Y and X are two independent but not identically distributed Rayleigh distribution under squared error loss function.