Makarand V. Ratnaparkhi

On discrete weighted distributions and their use in model choice for observed data

This paper provides a brief structural perspective of discrete weighted distributions in theory and practice.. It develops a unified view of previous work involving univariate and bivariate models with some new results pertaining to mixtures, form-invariance and Bayesian inference

An application of lomax distributions in receiver operating characteristic(roc)curve analysis

Receiver operating characteristic(ROC)curves are useful for studying the performance of diagnostic tests. ROC curves occur in many fields of applications including psychophysics, quality control and medical diagnostics. In practical situations, often the responses to a diagnostic test are classified into a number of ordered categories. Such data are referred to as ratings data. It is typically assumed that the underlying model is based on a continuous probability distribution. The ROC curve is then constructed from such data using this probability model. Properties of the ROC curve are inherited from the model. Therefore, understanding the role of different probability distributions in ROC modeling is an interesting and important area of research. In this paper the Lomax distribution is considered as a model for ratings data and the corresponding ROC curve is derived. The maximum likelihood estimation procedure for the related parameters is discussed. This procedure is then illustrated in the analysis of ...

On the functional relationship between entropy and variance with related applications

The functional relationship between entropy and variance is investigated for some well-known distributions. The distributions considered here are the reparameterized versions of the original forms. Such a reparameterization is necessary as in each case we have a common variance. The related graphs of entropy as a function of variance are used for certain comparisons. Further, within the class of distributions having a common variance, a measure of affinity between these distributions is proposed using entropy. A few aspects of the sampling distributions of an estimator of entropy, when the samples are either from the normal or from the exponential distributions, are discussed with a view to possible applications in the testing of hypotheses for related parameters

[4] Estimation of the number of monoclonal hybridomas in a cell-fusion experiment

Publisher Summary This chapter discusses the estimation of the number of monoclonal hybridomas in a cell-fusion experiment. It presents a simple method for the estimation of the proportion of the cultures with dividing cells that are monoclonal. This method is applicable after the population of fused cells has been fractionated into a large number of cultures by limiting dilution. The method is based on the Poisson probability model and assumes that the only information available to the investigator is the number of culture wells with dividing hybridoma cells of the total number of wells planted. The chapter explains the procedure that illustrates that the clonal growth in a culture well depends on the number of hybrid cells surviving in that dish. Therefore, it is appropriate to consider a probability model for the number of surviving hybridomas in a culture well and use the same for the estimation procedure. Such a probability model, owing to the typical nature of the available date (only a single observation representing the number of wells with and without hybridoma growth is available), has to be based on the knowledge of the experimental units (hybrid cells in a suspension and their survival process).

Uniform occurrence of digits for folded and mixture distributions on finite intervals

Historically, the occurrences of digits in a set of observed values of a random variable are of interest in theoretical and applied statistics for various reasons including rounding errors and statistical forensics. A probabilistic approach to such occurrences is needed in order to draw conclusions about the phenomena represented by these observed values. In this paper, we study certain structural properties of finite decimal expansions of real numbers from finite intervals within the framework of 10 k -folded distributions defined on such intervals. To provide a probabilistic structure for the occurrence of digits we obtain characterization results for the rectangular and folded-rectangular distributions. A brief discussion of the use of 10 k -bin histogram distributions to determine the approximate distribution of digits, along with two examples, illustrate our result.

Lognormal distribution - model for fatigue life and residual strength of composite materials

The differential equation of Yang for residual strength degradation in composite materials subject to fatigue loading is considered for obtaining the lognormal distribution as a model for the fatigue life of a composite material. Using this model, an ad-hoc method for estimating the physical parameters of the composite system is suggested. An example illustrates the use of our method in analyzing data. Since Yangs differential equation is for composite materials, our objective was to derive a model for composite materials. However, the methodology can be extended to other metals and materials.

Improving the Efficiency of the Two-stage Shrinkage Estimators Using Bootstrap Methods

In this paper, the applications of bootstrap methods in two-stage shrinkage estimation are discussed for the estimation of the mean of a normal distribution. The two-stage procedures are useful for increasing the efficiency of estimators. It is well known that the choice of the shrinkage factor plays an important role in related estimation procedures. In particular, the efficiency of the shrinkage estimator depends on the choice of shrinkage factor. The bootstrap methodology, due to its generality, is a useful tool in estimation problems. Therefore, in this paper, we have studied the interplay between these three methodologies for increasing the efficiency of the estimators of the normal mean. To our knowledge, such studies have not appeared in the literature. Further, using simulations we have shown that our methodology has a potential for controlling the efficiency of a given two-stage shrinkage estimator. Therefore, our methodology could be used effectively for analyzing the available sample data.

ANALYZING THE CENSORED LIFE DATA ARISING IN FRACTIONAL FACTORIAL DESIGNS: SPIN-ON-FILTER CASE STUDY

Choice of the best factors for increasing the dynamic life of a spin-on-filter for lubricants and fuels is discussed. A fractional factorial experiment on eight process variables collected data on the dynamic life of manufactured filters. Both complete ..