Untransformed first observation problem in regression model with moving average process

This paper shows the impact of underestimation of variance of an estima-tor when first observation is left untransformed to simplify the computational procedure. In fact, the bias of the variance is not diminishing even for large sample size for the model considered. By partitioning the covariance matrix into two parts, this paper explains why least square estimator with untrans-formed first observation shows such a consequence. To demonstrate this, an exact GLS estimator is developed by modifying an approximate estimator. Nonetheless, the computational simplicity remains same.     

Higher order moments of order statistics from the Lindley distribution and associated inference

ABSTRACT

The Lindley distribution is an important distribution for analysing the stress–strength reliability models and lifetime data. In many ways, the Lindley distribution is a better model than that based on the exponential distribution. Order statistics arise naturally in many of such applications. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the Lindley distribution. Then, we use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale parameters based on Type-II right-censored samples. Next, we use these results to determine the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics to develop Edgeworth approximate confidence intervals of the location and scale Lindley parameters. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.     

The bivariate logarithmic series distribution

The bivariate logarithmic series distribution was introduced by Subrahmaniam (1966) as a Fisher-limit to the bivariate negative binomial distribution. The present paper considers the properties of the distribution along with various models giving rise to it. Problems of estimation and the goodness-of-fit are examined. Methods for simulating the distribution are developed and illusuated.     

General saddlepoint approximations to distributions under an elliptical population

General saddlepoint approximations are derived for the distributions of statistics under an elliptical population. The technique is applied to obtain the tail probabilities of latent roots of a sample covariance matrix. It is shown that the method based on normalizing transformations by Tsuchiya and Konishi (1997) is efficient for the sample correlation coefficient in an elliptical sample.     

Approximate variances for tolerance-distribution free ld50-estimators supplemented with abbott's correction

This paper is concerned with the 'tolerance-distribution free estimation of a LD50 (LC50) in a toxicity experiment with background mortality. Firstly the observed proportions mortality are adjusted by Abbott's formula. The LD50 is then obtained by inserting the adjusted proportions in the usual formula, but the variance formula is adapted to account for the variability in the background mortality.     

Randomization with non-uniform allocations: fulfillment time distributions and bias properties

This article compares the properties of two balanced randomization schemes with several treatments under non-uniform allocation probabilities. According to the first procedure, the so-called truncated multinomial randomization design, the process employs a given allocation distribution, until a treatment receives its quota of subjects, after which this distribution switches to the conditional distribution for the remaining treatments, and so on. The second scheme, the random allocation rule, selects at random any legitimate assignment of the given number of subjects per treatment. The behavior of these two schemes is shown to be quite different: the truncated multinomial randomization design's assignment probabilities to a treatment turn out to vary over the recruitment period, and its accidental bias can be large, whereas the random allocation rule's this bias is bounded. The limiting distributions of the instants at which a treatment receives the given number of subjects is shown to be that of weighted spacings for normal order statistics with different variances. Formulas for the selection bias of both procedures are also derived.     

Efficient sample size allocation with cost constraints for heterogeneous-variance group comparison

When conducting research with controlled experiments, sample size planning is one of the important decisions that researchers have to make. However, current methods do not adequately address this issue with regard to variance heterogeneity with some cost constraints for comparing several treatment means. This paper proposes a sample size allocation ratio in the fixed-effect heterogeneous analysis of variance when group variances are unequal and in cases where the sampling and/or variable cost has some constraints. The efficient sample size allocation is determined for the purpose of minimizing total cost with a designated power or maximizing the power with a given total cost. Finally, the proposed method is verified by using the index of relative efficiency and the corresponding total cost and the total sample size needed. We also apply our method in a pain management trial to decide an efficient sample size. Simulation studies also show that the proposed sample size formulas are efficient in terms of statistical power. SAS and R codes are provided in the appendix for easy application.     

Correction

In many probability and mathematical statistics courses the probability generating function (PGF) is typically overlooked in favor of the more utilized moment generating function. However, for certain types of random variables, the PGF may be more appealing. For example, sums of independent, non-negative, integer-valued random variables with finite support are easily studied via the PGF. In particular, the exact distribution of the sum can easily be calculated. Several illustrative classroom examples, with varying degrees of difficulty, are presented. All of the examples have been implemented using the R statistical software package.     

A simple approach to the estimation of Tukey's gh distribution

ABSTRACT

The Tukey's gh distribution is widely used in situations where skewness and elongation are important features of the data. As the distribution is defined through a quantile transformation of the normal, the likelihood function cannot be written in closed form and exact maximum likelihood estimation is unfeasible. In this paper we exploit a novel approach based on a frequentist reinterpretation of Approximate Bayesian Computation for approximating the maximum likelihood estimates of the gh distribution. This method is appealing because it only requires the ability to sample the distribution. We discuss the choice of the input parameters by means of simulation experiments and provide evidence of superior performance in terms of Root-Mean-Square-Error with respect to the standard quantile estimator. Finally, we give an application to operational risk measurement.     

The bahadur efficiency of paired versus joint ranking procedures for pa1rwtse multiple comparisons

The performance of paired versus joint ranking procedures for pairwise multiple comparisons is investigated using approxiirete Bahadur efficiency, When the populations to be compared are widely separated, or-when the. data arise from a shift model with an underlying unimodal density, the paired ranking procedure is found to be better for comparing two adjacent populations while the joint ranking procedure is more efficient for comparing the two most distant populations