Model Assisted Statistics and Applications

The paper deals with the estimation problem of Poisson type Exponential Class model which has wide application in software reliability. This model consists of two parameters namely, the total number of failures and the failure rate. Considering the behaviour of the parameter, total number of failure and limitation of Poisson distribution, a generalized Poisson distribution has been proposed as a prior for this parameter. Further, an inverted Gamma prior has been selected for failure rate in view of its property. The Bayes estimators have been obtained considering these priors under Squared Error Loss Function. To study the performance of obtained estimators, these estimators have been compared with corresponding maximum likelihood estimators on the basis of a Monte Carlo simulation study.

This paper considers and compares Classical (Student-t, Johnson-t, Median-t, Mad-t), Bootstrap (Bootstrap-t, Bias-corrected Accelerated Bootstrap) and Transformations ( T 1 , T 3 , Median T 1 and Median T 3 ) approaches to find confidence intervals for estimating the mean of an asymmetrical distribution with unknown standard deviation. A simulation study has been made to compare the performance of the interval estimators by using average widths and coverage probabilities as performance estimators. For highly skewed distributions T 1 , Median T 1 , T 3 and Median T 3 outperform other intervals in terms of coverage probability attaining the nominal. However, Mad-t, Mad T 1 , Mad T 3 , bootstrap-t and BCA performed better compared to others in the sense of shorter widths. It is also noted that the proposed Median T 1 , Median T 3 , Mad t, Mad T 1 and Mad T 3 intervals are handy and easy to implement compared to others. Some health related data are considered to illustrate the findings of the paper. This paper gives more choices to use best possible interval estimators among many that have been used by several researchers.

When Lorenz curves cross, conditional coefficient of variation curve can be used to test the inequality dominance. In the present paper, confidence bands are provided for conditional coefficient of variation curve. Based on these confidence bands a multiple comparison test is proposed for testing the dominance of conditional coefficient of variation curve. The power of the test is computed and a real life illustration is given at the end.

The mathematical theory of tolerance intervals for distributions with Poisson outcomes is well developed. One criticism is the relative difficulty of computing the Poisson tolerance intervals, particularly when approximate formulae are not applicable. We offer the computational algorithm for the exact upper and lower tolerance intervals founded on the estimate of the exact confidence limits for the Poisson rate. Thus the exact tolerance intervals may be calculated using StatXact. To illustrate the algorithm, we apply it to the analysis of transfusion – associated deaths.

Sensitivity and specificity of an investigational qualitative diagnostic test are conventionally estimated by comparing with an existing qualitative reference test which is often imperfect and hence introduces misclassification biases to sensitivity and specificity estimates. In many situations, both tests measure an underlying continuous trait associated with a specific disease/virus and report binary results by comparing the measurement to a pre-determined cutoff point. The maximum likelihood estimates of the sensitivity and specificity are established under independent normal assumption between the underlying trait and measurement errors for both investigational test and reference test. This allows us to avoid misclassificiation biases caused by imperfect reference test without retesting any subjects.

Estimation of the population average in a finite population by means of sampling strategy dependent on the sample quantile of an auxiliary variable is considered. The sampling design is proportionate to the difference of two quantiles of an auxiliary variable. The sampling scheme implementing the sampling design is proposed. The derived inclusion probabilities are applied to estimation the population mean using the well known Horvitz-Thompson estimator. Moreover, the regression estimator is defined as the function of the slope coefficient dependent on the quantiles of the auxiliary variable.

Various estimators of the population median were compared for small samples (N ⩽ 50). The competitors included the sample median, Harrell-Davis (HD) estimate, six new estimates (Circle, DblExp, Exp+, Exp-, AltExp, Fibon) that require no à priori information about the population, and one estimate (AllExp) that requires information on the general form of the distribution The two benchmark criteria were the mean square error (MSE) and the rank based error (RBE). When there is no information available on the population, (a) AltExp was the best estimator for N ⩽ 30 for the MSE criterion, (b) the estimate based on the Fibonacci sequence was the best for N ⩽ 30 for the RBE criterion, and (c) the Harrell-Davis estimator was superior for N > 30. There was no support for using the sample median as an estimate of the population median.