• Title/Summary/Keyword: mean and variance

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On Estimating the Variance of a Normal Distribution With Known Coefficient of Variation

  • Ray, S.K.;Sahai, A.
    • Journal of the Korean Statistical Society
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    • v.7 no.2
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    • pp.95-98
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    • 1978
  • This note deals with the estimations of the variance of a normal distribution $N(\theta,c\theta^2)$ where c, the square of coefficient of variation is assumed to be known. This amounts to the estimation of $\theta^2$. The minimum variance estimator among all unbiased estimators linear in $\bar{x}^2$ and $s^2$ where $\bar{x}$ and $s^2$ are the sample mean and variance, respectively, and the minimum risk estimator in the class of all estimators linear in $\bar{x}^2$ and $s^2$ are obtained. It is shown that the suggested estimators are BAN.

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Compromised feature normalization method for deep neural network based speech recognition (심층신경망 기반의 음성인식을 위한 절충된 특징 정규화 방식)

  • Kim, Min Sik;Kim, Hyung Soon
    • Phonetics and Speech Sciences
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    • v.12 no.3
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    • pp.65-71
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    • 2020
  • Feature normalization is a method to reduce the effect of environmental mismatch between the training and test conditions through the normalization of statistical characteristics of acoustic feature parameters. It demonstrates excellent performance improvement in the traditional Gaussian mixture model-hidden Markov model (GMM-HMM)-based speech recognition system. However, in a deep neural network (DNN)-based speech recognition system, minimizing the effects of environmental mismatch does not necessarily lead to the best performance improvement. In this paper, we attribute the cause of this phenomenon to information loss due to excessive feature normalization. We investigate whether there is a feature normalization method that maximizes the speech recognition performance by properly reducing the impact of environmental mismatch, while preserving useful information for training acoustic models. To this end, we introduce the mean and exponentiated variance normalization (MEVN), which is a compromise between the mean normalization (MN) and the mean and variance normalization (MVN), and compare the performance of DNN-based speech recognition system in noisy and reverberant environments according to the degree of variance normalization. Experimental results reveal that a slight performance improvement is obtained with the MEVN over the MN and the MVN, depending on the degree of variance normalization.

Determination of the Optimal Process Mean and Upper Limit with considering the rpm(rate per minute) (rpm 변화를 고려한 최적의 공정 평균과 상한 규격의 결정)

  • 송우복;안광일;김성집
    • Journal of Korean Society for Quality Management
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    • v.26 no.1
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    • pp.61-73
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    • 1998
  • The quality control literature contains a substantial number of articles concerned with how to optimally choose control limits in order to minimize production cost. The purpose of the this study is to determine the economic setting for the process mean of an industrial process. In this study it is assumed that the lower control limit is set by government regulations and the u, pp.r limit and process mean are chosen based on economic considerations. Much research has been conducted on this problem under the condition of the fixed rpm(rate per minute). However a variance can be increased in proportion to the level of rpm and the increase of the variance can change the optimal process mean. Therefore, it is desirable to determine both the process mean and the level of rpm simultaneously. In this paper, a mathematical model is presented which considers the u, pp.r limit and the rpm as variables.

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Variance estimation of a double expanded estimator for two-phase sampling

  • Mingue Park
    • Communications for Statistical Applications and Methods
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    • v.30 no.4
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    • pp.403-410
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    • 2023
  • Two-Phase sampling, which was first introduced by Neyman (1938), has various applications in different forms. Variance estimation for two-phase sampling has been an important research topic because conventional variance estimators used in most softwares are not working. In this paper, we considered a variance estimation for two-phase sampling in which stratified two-stage cluster sampling designs are used in both phases. By defining a conditionally unbiased estimator of an approximate variance estimator, which is calculable when all elements in the first phase sample are observed, we propose an explicit form of variance estimator of the double expanded estimator for a two-phase sample. A small simulation study shows the proposed variance estimator has a negligible bias with small variance. The suggested variance estimator is also applicable to other linear estimators of the population total or mean if appropriate residuals are defined.

Acoustic analysis of fricatives in dysarthric speakers with cerebral palsy

  • Hernandez, Abner;Lee, Ho-young;Chung, Minhwa
    • Phonetics and Speech Sciences
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    • v.11 no.3
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    • pp.23-29
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    • 2019
  • This study acoustically examines the quality of fricatives produced by ten dysarthric speakers with cerebral palsy. Previous similar studies tend to focus only on sibilants, but to obtain a better understanding of how dysarthria affects fricatives we selected a range of samples with different places of articulation and voicing. The Universal Access (UA) Speech database was used to select thirteen words beginning with one of the English fricatives (/f/, /v/, /s/, /z/, /ʃ/, /ð/). The following four measurements were taken for both dysarthric and healthy speakers: phoneme duration, mean spectral peak, variance and skewness. Results show that even speakers with mild dysarthria have significantly longer fricatives and a lower mean spectral peak than healthy speakers. Furthermore, mean spectral peak and variance showed significant group effects for both healthy and dysarthric speakers. Mean spectral peak and variance was also useful for discriminating several places of articulation for both groups. Lastly, spectral measurements displayed important group differences when taking severity into account. These findings show that in general there is a degradation in the production of fricatives for dysarthric speakers, but difference will depend on the severity of dysarthria along with the type of measurement taken.

Selection of Data-adaptive Polynomial Order in Local Polynomial Nonparametric Regression

  • Jo, Jae-Keun
    • Communications for Statistical Applications and Methods
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    • v.4 no.1
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    • pp.177-183
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    • 1997
  • A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

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An estimator of the mean of the squared functions for a nonparametric regression

  • Park, Chun-Gun
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.3
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    • pp.577-585
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    • 2009
  • So far in a nonparametric regression model one of the interesting problems is estimating the error variance. In this paper we propose an estimator of the mean of the squared functions which is the numerator of SNR (Signal to Noise Ratio). To estimate SNR, the mean of the squared function should be firstly estimated. Our focus is on estimating the amplitude, that is the mean of the squared functions, in a nonparametric regression using a simple linear regression model with the quadratic form of observations as the dependent variable and the function of a lag as the regressor. Our method can be extended to nonparametric regression models with multivariate functions on unequally spaced design points or clustered designed points.

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Lead Time Analysis for Transportation Mode Decision Making (輸送手段의 選擇을 위한 리드타임 分析)

  • 문상원
    • Journal of the Korean Operations Research and Management Science Society
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    • v.13 no.1
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    • pp.47-47
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    • 1988
  • Rapid globalization of production and marketing functions makes choice of international transportation mode of great importance. In this paper, transportation mode is characterized by two factors, mean and variability of transportation lead time. We developed a simple mathematical model to estimate the relative impact of mean lead time, lead time variance and demand variance on the required average inventory level under specified service rates.

Design Criterion for Estimating Mean and Variance Functions

  • Lim, Yong B.
    • International Journal of Quality Innovation
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    • v.1 no.1
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    • pp.32-37
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    • 2000
  • In an industrial process, the proper objective is to find the optimal operating conditions with minimum process variability around the target. Vining and Myers(1990) suggest to use the separate model for the mean response and the process varian linear predictor ${\tau}_i={\log}\;{\sigma}^2_i$ is unknown and should be estimated. Noting that the variance of $\hat{{\tau}_i}$ is heterogeneous, another appropriate D-optimality criterion $D_3$ based on the method of generalized least squares is proposed in this paper.

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Theoretical Basis of PERT Formula and a New Estimation Method (PERT 공식의 이론적 근거와 새로운 추정방법)

  • Kim, Se-Hun;Won, Y.K.;Chae, Kyung-C.
    • Journal of Korean Institute of Industrial Engineers
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    • v.15 no.2
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    • pp.103-108
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    • 1989
  • PERT formulae for the mean and variance of activity time are near exact only over a short interval of the concentration parameter which is defined as the sum of the two shape parameters of the beta distribution. Aiming a better estimation of the mean and variance of activity time, we propose a method of subjectively estimating this concentration parameter via estimating the probability of completing the activity within a specified time interval.

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