• Communications for Statistical Applications and Methods
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• v.6 no.2
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• pp.543-564
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• 1999

The principal aim of a sequential phase I clinical trial in which the toxicity reponses of a group of patient(s) determine the dose level of the next patient(s) group is to estimate the maximal tolerated dose(MTD) of a new drug, In this paper we compared with a simulation study the performance of the MTD estimates that are determined by a stopping rule in a design and also those that are determined by analyzing the data after a clinical trial is terminated. To the latter belong the mean median mode and maximum likelihood estimates. For the Standard Methods the stopping rule MTD is quite inefficient but the median MTD has a best efficiency and is robust with respect to the three different toxicity curves. The problem of non-convergence of MLE MTD is severe. A more improved MTD estimate is produced by combining the advantages of the various MTD estimates and its efficiency is better than the single median MTD estimate especially for the toxicity curve of an unlucky choice of dose levels. The simulation results suggest that simple types of phase I designs can be combined with relatively standard analytic techniques to provide a more efficient MTD estimate.

• Journal of the Korean Data and Information Science Society
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• v.23 no.2
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• pp.411-417
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• 2012

In this paper, we consider the estimation of multinomial proportions. Multinomial distribution is the most important multivaritate distribution. Estimation of multinomial parameters for multinomial distribution is widely applicable to many practical research areas including genetics. We investigated the properties of several frequency substitution estimates and derived the maximum likelihood estimate of multinomial proportions of Hardy Weinberg proportions. Phenotype and genotype frequencies of allele are used to the estimation of multinomial proportions. These estimates are then analyzed via numerical data. Small sample Monte Carlo simulation is conducted to compare considered estimates of multinomial proportions.

• Asian-Australasian Journal of Animal Sciences
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• v.12 no.5
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• pp.677-681
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• 1999

Estimates were made of genetic parameters for average daily gain (ADG) and average backfat thickness (ABF), and of the effect of sex on estimates of variance-covariance components for average daily gain of boars (DGM) and gilts (DGF) and average bacfat thickness of boars (BFM) and gilts (BFF) by residual maximum likelihood (REML) under a bivariate animal model. Data included a total of 2233 records (757 for boars and 1476 for gilts) of the Large White breed born between 1981 and 1986 in Miyazaki and Iwate prefectures in Japan. Heritability estimates for ADG and ABF were 0.43 and 0.69, respectively, with a genetic correlation of -0.08. Heritability estimates for DGM and DGF were 0.54 and 0.46, respectively, with a genetic correlation of 0.79, including that the two traits are influenced by similar but not identical genes. Respective estimates for BFM and BFF were 0.71 and 0.72 with a genetic correlation of 0.95, indicating that identical genes influence backfat thickness in boars and gilts.

• Journal of Navigation and Port Research
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• v.37 no.5
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• pp.453-461
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• 2013

This paper describes evaluation procedures and experimental results for the estimation of Cumulative Distribution Functions (CDF) giving best-fit to the sample data in the Probability based risk Evaluation Techniques (PET) which is to assess the risks of a small-sized sea floater. The CDF in the PET is to provide the reference values of risk acceptance criteria which are to evaluate the risk level of the floater and, it can be estimated from sample data sets of motion response functions such as Roll, Pitch and Heave in the floater model. Using Maximum Likelihood Estimates and with the eight kinds of regulated distribution functions, the evaluation tests for the CDF having maximum likelihood to the sample data are carried out in this work. Throughout goodness-of-fit tests to the distribution functions, it is shown that the Beta distribution is best-fit to the Roll and Pitch sample data with smallest averaged probability errors $\bar{\delta}(0{\leq}\bar{\delta}{\leq}1.0)$ of 0.024 and 0.022, respectively and, Gamma distribution is best-fit to the Heave sample data with smallest $\bar{\delta}$ of 0.027. The proposed method in this paper can be expected to adopt in various application areas estimating best-fit distributions to the sample data.

• Asian-Australasian Journal of Animal Sciences
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• v.13 no.5
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• pp.575-579
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• 2000

First lactation records of 683 Murrah buffaloes maintained at NDRI, Karnal which were progeny of 84 sires used for comparing the heritability estimates of age at first calving, first lactation milk yield and first service period under single and multiple trait models using restricted maximum likelihood (REML) method of estimation under an individual animal model. The results indicated that the heritability estimates may vary under single and multiple trait models depending upon the magnitude of genetic and environmental correlation among the traits being considered. Therefore, a single or multiple trait model is recommended for estimation of variance components depending upon the goal of breeding programme. However, there may not be any advantage of considering a trait with zero or near zero heritability and having no or very low genetic correlation with other traits in the model. Lower heritability estimates of part lactation yield (120-day milk yield) implied that there may not be any advantage of considering this trait in place of actual 305-day milk yield, whereas, comparable heritability estimates of predicted 305-day milk yield suggested that it could be used for sire evaluation to reduce the cost of milk recording under field conditions.

• The Korean Journal of Applied Statistics
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• v.9 no.2
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• pp.119-134
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• 1996

Accelerated life testing (ALT) of a system is commonly used to reduce time and cost. ALT is achieved by subjecting the test systems to more severe conditions than the normal ones to obtain estimates of life distribution under normal condition. The major interest of this research is to use a model of incorporating the common environmental effect on the components serially linked into a system-so called frailty model for the system life time distribution under each stress and to discuss the related data analysis and comparison of the model with the generally used one. The profile likelihood is used to get an initial values required to compute maximum likelihood estimates and simulation is carried for comparison.

• Asian-Australasian Journal of Animal Sciences
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• v.23 no.8
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• pp.981-986
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• 2010

Genetic parameters of growth traits were estimated in the German Angora rabbit reared in the sub-temperate region of India. Estimates of (co)variance components were obtained for body weights at weaning (42 days) and post-weaning at 84, 126 and 168 days. A total of 8,324 animal records were used for the analysis of these traits. The data were analyzed by restricted maximum likelihood (REML) fitting six animal models with various combinations of direct and maternal effects. A log likelihood ratio test was used to select the most appropriate univariate model for each trait. Direct heritability estimates were observed to be moderate for the traits under study. Heritability estimates for weaning (42 d), 84, 126 and 168 d weights obtained from the best models were $0.25{\pm}0.05$, $0.17{\pm}0.05$, $0.21{\pm}0.06$ and $0.12{\pm}0.05$. Maternal effects had higher importance at weaning, and declined with the advancement of age. Significant maternal permanent environmental effect on weaning and post-weaning weights was a carryover effect of maternal influences during pre-weaning age. The estimated repeatabilities of doe effects on body weights were 0.37, 0.22, 0.18 and 0.28 at weaning, 84, 126 and 168 d body weight, respectively. Results indicated that modest rate of genetic progress is possible for body weight traits of Angora rabbit through selection. Similarly, these growth traits could be included in selection criteria along with wool traits for early selection of the animals.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.289-298
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• 1998

We investigate the distribution of likelihood ratio test(LRT) of null hypothesis a sample is from single gamma with unknown shape and scale against the alternative hypothesis a sample is from a mixture of two gammas, each with unknown scale and unknown (but equal) scale. To obtain stable maximum likelihood estimates(MLE) of a mixture of two gamma distributions, the EM(Dempster, Laird, and Robin(1977))and Modified Newton(Jensen and Johansen(1991)) algorithms were implemented. Based on EM, we made a simple structure likelihood equation for each parameter and could obtain stable solution by Modified Newton Algorithms. Simulation study was conducted to investigate the distribution of LRT for sample size n = 25, 50, 75, 100, 50, 200, 300, 400, 500 with 2500 replications. To determine the small sample distribution of LRT, I considered the model of a gamma distribution with shape parameter equal to 1 + f(n) and scale parameter equal to 2. The simulation results indicate that the null distribution is essentially invariant to the value of the shape parameter. Modeling of the null distribution indicates that it is well approximated by a gamma distribution with shape parameter equal to the quantity $0.927+1.18/\sqrt{n}$ and scale parameter equal to 2.16.

• Korean Journal of Hydrosciences
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• v.6
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• pp.13-22
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• 1995

The augmenting hydrologic data using a correlation procedure has been used to improve the estimates of the mean and variance at the site of interest with short record when one or more near by sites with longer records are available. The variance of the unbiased maximum likelihood estimator of $ derived by Moran based on the multivariate normal distribytion is modified into the form of Matalas and Jacobs for the biveriate normal distribution to get the critical minimum values of the multiple correlation coefficient which give the improvement for estimating the variance at the site of interest. Those values are tabulated for various lengths of short records and the number of sites.

• The Korean Journal of Applied Statistics
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• v.10 no.2
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• pp.325-338
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• 1997

This paper suggests a sequence of dependence models as a statistical analysis model for vaccination data on chickenpox and discusses a method for evaluating maximum likelihood estimates of unknown parameters in the suggested model.