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Poisson Parameters of Antimicrobial Activity: A Quantitative StructureActivity Approach
, 2012
"... Abstract: A contingency of observed antimicrobial activities measured for several compounds vs. a series of bacteria was analyzed. A factor analysis revealed the existence of a certain probability distribution function of the antimicrobial activity. A quantitative structureactivity relationship ana ..."
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Abstract: A contingency of observed antimicrobial activities measured for several compounds vs. a series of bacteria was analyzed. A factor analysis revealed the existence of a certain probability distribution function of the antimicrobial activity. A quantitative structureactivity relationship analysis for the overall antimicrobial ability was conducted using the population statistics associated with identified probability distribution function. The antimicrobial activity proved to follow the Poisson distribution if just one factor varies (such as chemical compound or bacteria). The Poisson parameter estimating antimicrobial effect, giving both mean and variance of the antimicrobial activity, was used to develop structureactivity models describing the effect of compounds on bacteria and fungi species. Two approaches were employed to obtain the models, and for every approach, a model was selected, further investigated and found to be statistically significant. The best predictive model for antimicrobial effect on bacteria and fungi species was identified using graphical representation of observed vs. calculated values as well as several predictive power parameters.
Discriminating Between the LogNormal and LogLogistic Distributions
 Communications in Statistics  Theory and Methods
, 2010
"... Lognormal and loglogistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution funct ..."
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Lognormal and loglogistic distributions are often used to analyze lifetime data. For certain ranges of the parameters, the shape of the probability density functions or the hazard functions can be very similar in nature. It might be very difficult to discriminate between the two distribution functions. In this paper, we consider the discrimination procedure between the two distribution functions. We use the ratio of maximized likelihood for discrimination purposes. The asymptotic properties of the proposed criterion have been investigated. It is observed that the asymptotic distributions are independent of the unknown parameters. The asymptotic distributions have been used to determine the minimum sample size needed to discriminate between these two distribution functions for a user specified probability of correct selection. We have performed some simulation experiments to see how the asymptotic results work for small sizes. For illustrative purpose two data sets have been analyzed.
Discriminating Between The Normal and The Laplace Distributions
"... Both normal and Laplace distributions can be used to analyze symmetric data. In this paper we consider the logarithm of the ratio of the maximized likelihoods to discriminate between the two distribution functions. We obtain the asymptotic distributions of the test statistics and it is observed that ..."
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Both normal and Laplace distributions can be used to analyze symmetric data. In this paper we consider the logarithm of the ratio of the maximized likelihoods to discriminate between the two distribution functions. We obtain the asymptotic distributions of the test statistics and it is observed that they are independent of the unknown parameters. If the underlying distribution is normal the asymptotic distribution works quite well even when the sample size is small. But if the underlying distribution is Laplace the asymptotic distribution does not work well for the small sample sizes. For the later case we propose a bias corrected asymptotic distribution and it works quite well even for small sample sizes. Based on the asymptotic distributions, minimum sample size needed to discriminate between the two distributing functions is obtained for a given probability of correct selection. Monte Carlo simulations are performed to examine how the asymptotic results work for small sizes and two data sets are analyzed for illustrative purposes.
Discriminating Among the LogNormal, Weibull and Generalized Exponential Distributions
"... In this paper we consider the model selection / discrimination among the three important lifetime distributions. All these three distributions have been used quite e®ectively to analyze lifetime data in the reliability analysis. We study the probability of correct selection using the maximized likel ..."
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In this paper we consider the model selection / discrimination among the three important lifetime distributions. All these three distributions have been used quite e®ectively to analyze lifetime data in the reliability analysis. We study the probability of correct selection using the maximized likelihood method, as it has been used in the literature. We further compute the asymptotic probability of correct selection and compare the theoretical and simulation results for di®erent sample sizes and for di®erent model parameters. The results have been extended for TypeI censored data also. The theoretical and simulation results match quite well. Two real data sets have been analyzed for illustrative purposes. We also suggest a method to determine the minimum sample size required to discriminate among the three distributions for a given probability of correct selection and a user speci¯ed protection level.
Discrimination between Gamma and LogNormal Distributions by Ratio of Minimized KullbackLeibler Divergence
"... The Gamma and LogNormal distributions are frequently used in reliability to analyze lifetime data. The two distributions overlap in many cases and make it difficult to choose the best one. The ratio of maximized likelihood (RML) has been extensively used in choosing between them. But the KullbackL ..."
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The Gamma and LogNormal distributions are frequently used in reliability to analyze lifetime data. The two distributions overlap in many cases and make it difficult to choose the best one. The ratio of maximized likelihood (RML) has been extensively used in choosing between them. But the KullbackLeibler information is a measure of uncertainty between two functions, hence in this paper, we examine the use of KullbackLeibler Divergence (KLD) in discriminating either the Gamma or LogNormal distribution. Therefore, the ration of minimized KullbackLeibler Divergence (RMKLD) test statistic is introduced and its applicability will be explained by two real data sets. Although the consistency of the new test statistic with RML is convinced, but the KLD has higher probability of correct selection when the null hypothesis is Gamma.