• Journal of Integrative Natural Science
• /
• v.14 no.3
• /
• pp.123-129
• /
• 2021

This research examines the effect of positively skewed population distribution on the two sample t-test through simulation. For simulation work, two independent samples were selected from the same chi-square distributions with 3, 5, 10, 15, 20, 30 degrees of freedom and sample sizes 3, 5, 10, 15, 20, 30, respectively. Chi-square distribution is largely skewed to the right at small degrees of freedom and getting symmetric as the degrees of freedom increase. Simulation results show that the sampled populations are distributed positively skewed like chi-square distribution with small degrees of freedom, the F-test for the equality of variances shows poor performances even at the relatively large degrees of freedom and sample sizes like 30 for both, and so it is recommended to avoid using F-test. When two population variances are equal, the skewness of population distribution does not affect on the t-test in terms of the confidence level. However even though for the highly positively skewed distribution and small sample sizes like three or five the t-test achieved the nominal confidence level, the error limits are very large at small sample size. Therefore, if the sampled population is expected to be highly skewed to the right, it will be recommended to use relatively large sample size, at least 20.

• Journal of the Korean Statistical Society
• /
• v.23 no.1
• /
• pp.135-149
• /
• 1994

We discussed a comparison of distribution-free two-sample procedures based on placements or ranks. Iterative asymptotic distribution of both two-sample procedures is studies and small sample Monte Carlo simulation results are presented. Also, we proposed the Hodges-Lehmann type location estimator based on linear placement statistics.

• Journal of the Korean Data and Information Science Society
• /
• v.23 no.6
• /
• pp.1271-1277
• /
• 2012

In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

• Communications for Statistical Applications and Methods
• /
• v.16 no.2
• /
• pp.349-361
• /
• 2009

In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Journal of the Korea Safety Management & Science
• /
• v.9 no.3
• /
• pp.165-171
• /
• 2007

Dependent models in quality statistics are classified as serially autocorrelated model, multivariate model and dependent sample model. Dependent sample model is most efficient in time and cost to obtain samples among the above models. This paper proposes to implement parametric and nonparametric models into production system depended on demand pattern. Nonparametric models have distribution free and asymptotic distribution free techniques. Quality statistical models are classified into two categories ; the number of dependent sample and the type of data. The type of data consists of nominal, ordinal, interval and ratio data. The number of dependent sample divides into 2 samples and more than 3 samples.

• Communications for Statistical Applications and Methods
• /
• v.19 no.3
• /
• pp.345-358
• /
• 2012

In a parametric sample selection model, the distribution assumption is critical to obtain consistent estimates. Conventionally, the normality assumption has been adopted for both error terms in selection and main equations of the model. The normality assumption, however, may excessively restrict the true underlying distribution of the model. This study introduces the $S_U$-normal distribution into the error distribution of a sample selection model. The $S_U$-normal distribution can accommodate a wide range of skewness and kurtosis compared to the normal distribution. It also includes the normal distribution as a limiting distribution. Moreover, the $S_U$-normal distribution can be easily extended to multivariate dimensions. We provide the log-likelihood function and expected value formula based on a bivariate $S_U$-normal distribution in a sample selection model. The results of simulations indicate the $S_U$-normal model outperforms the normal model for the consistency of estimators. As an empirical application, we provide the sample selection model for car ownership and a car expense relationship.

• Journal of the Korean Statistical Society
• /
• v.19 no.2
• /
• pp.139-144
• /
• 1990

For the first-order bilinear time series model $X_t = aX_{t-1} + e_i + be_{t-1}X_{t-1}$ where ${e_i}$ is a sequence of independent normal random variables with mean 0 and variance $\sigma^2$, the asymptotic distribution of sample autocarrelation function is obtained and shown to follow a normal distribution. The variance of the asymptotic distribution is of a complicated form and hence a bootstrap estimate of the variance is proposed for large sample inference. This result can be used to distinguish between different bilinear models.

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.249-259
• /
• 2002

In order to estimate the mean and variance for a Normal distribution which is truncated at both right and left sides, maximum likelihood estimators based on the entire sample from the original distribution are compared with the sample mean and variance of the censored sample which is the data remaining after truncation using simulation. We found that, surprisingly, the mean squared error of the mean based on the censored data Is smaller than that of the full sample estimators.

• The Korean Journal of Applied Statistics
• /
• v.11 no.2
• /
• pp.287-302
• /
• 1998

Saddlepoint approximation to the distribution function of sample mean(Daniels, 1987) is extended to the case of general statistic in this paper. The suggested approximation methods are applied to derive the approximations to the distributions of some statistics, including sample valiance and studentized mean. Some comparisons with other methods show that the suggested approximations are very accurate for moderate or small sample sizes. Even in extreme tail the accuracies are also maintained.

• The Mathematical Education
• /
• v.59 no.1
• /
• pp.47-62
• /
• 2020

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.