Some estimation procedures using a linear model in successive sampling

ABSTRACT

In successive sampling some recent works depict the use of super-population models where information on stable auxiliary variable over occasions has been utilized. Stability character of auxiliary variable may not sustain, if the duration between occasions is large. To cope with such situations, the present work is an attempt to develop some estimation procedures by utilizing the information on two independent auxiliary variables through a linear super-population model. Some estimators are proposed to estimate the current population mean in two occasions successive (rotation) sampling. Optimum replacement strategies are formulated and performances of the proposed estimators have been discussed. Results are interpreted through empirical studies.     

On the use of several auxiliary variables in estimation of current population mean in successive sampling

ABSTRACT

The present work intends to put emphasis on the role of several auxiliary variables on both the occasions to improve the precision of estimates at current occasion in two-occasion successive sampling. Utilizing the readily available information on several auxiliary variables on both occasions and the information on study variable from the previous occasion, an efficient estimation procedure of population mean on current occasion has been suggested. Optimum replacement strategy and the efficiencies of the proposed estimator have been discussed. Empirical studies are carried out, and appropriate recommendations have been put forward for practical applications.     

Bayesian prediction bounds for the pareto lifetime model

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let x₁ ≤ x₂ x₃ ≤…≤z_k denote the survival lifetimes of the first k of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of t h e remaining (n-k) businesses, using the conditional probability density function. Examples are given to illustrate our results.     

Setting the clock back to zero property of a class of bivariate life distributions

In a previous paper. B. R. Rao and Talwalker (1993) considered absolutely continuous life distributions and extended the Lack of Memory Property (L.M.P.) of the exponential distribution and showed that several classes of life distributions have this property, which was called the 'setting the clock back to zero' property. ¶Its analog is discussed in the present paper for hivariate and multivariate classes of life distributions. As a simple application of this analog, it is proved that the Life expectancy and the Percentile Residual Life vectors of a population of individuals under the influence of multiple competing risks have simple expressions if the class of their joint life distributions has the setting the clock back to zero property,     

Optimally robust estimators in generalized Pareto models

In this paper, we study the robustness properties of several procedures for the joint estimation of shape and scale in a generalized Pareto model. The estimators that we primarily focus upon, most bias robust estimator (MBRE) and optimal MSE-robust estimator (OMSE), are one-step estimators distinguished as optimally robust in the shrinking neighbourhood setting; that is, they minimize the maximal bias, respectively, on such a specific neighbourhood, the maximal mean squared error (MSE). For their initialization, we propose a particular location–dispersion estimator, MedkMAD, which matches the population median and kMAD (an asymmetric variant of the median of absolute deviations) against the empirical counterparts. These optimally robust estimators are compared to the maximum-likelihood, skipped maximum-likelihood, Cramér–von-Mises minimum distance, method-of-medians, and Pickands estimators. To quantify their deviation from robust optimality, for each of these suboptimal estimators, we determine the finite-sample breakdown point and the influence function, as well as the statistical accuracy measured by asymptotic bias, variance, and MSE – all evaluated uniformly on shrinking neighbourhoods. These asymptotic findings are complemented by an extensive simulation study to assess the finite-sample behaviour of the considered procedures. The applicability of the procedures and their stability against outliers are illustrated for the Danish fire insurance data set from the package evir.     

On the existence and uniqueness of the MLEs of the parameters of a general class of exponentiated distributions

In this paper, we present a formal simple proof for the existence and uniqueness of the maximum likelihood estimates (MLEs) of the parameters of a general class of exponentiated distributions. This class includes the exponentiated (general) exponential, exponentiated Rayleigh (scaled Burr X) and exponentiated Pareto distributions, as special cases, and thus the proof given here establishes the existence and uniqueness of the MLEs for these important special cases as well.     

Confidence regions for Pareto parameters from a single and independent samples

[Abstract] Based on a single and on two independent samples, joint confidence regions for parameters of Pareto distributions are proposed with minimum volume properties and without assigning the confidence level to dimensions. In the one-sample case, comparisons are made to former simultaneous confidence sets for Pareto parameters by means of simulation and a real data set. The two-sample case is studied in various set-ups and comprises simultaneous confidence regions for the shape parameters, the scale parameters, and higher-dimensional vectors of these parameters, where common shape and common scale models are also considered.     

Pareto mimic algorithm: An approach to the team orienteering problem

The team orienteering problem is an important variant of the vehicle routing problem. In this paper, a new algorithm, called Pareto mimic algorithm, is proposed to deal with it. This algorithm maintains a population of incumbent solutions which are updated using Pareto dominance. It uses a new operator, called mimic operator, to generate a new solution by imitating an incumbent solution. Furthermore, to improve the quality of a solution, it employs an operator, called swallow operator which attempts to swallow (or insert) an infeasible node and then repair the resulting infeasible solution. A comparative study supports the effectiveness of the proposed algorithm, especially, our algorithm can quickly find new better results for several large-scale instances. We also demonstrate that Pareto mimic algorithm can be generalized to solve other routing problems, e.g., the capacitated vehicle routing problem.     

Constants and variables: Pareto's asymmetric distribution curve

The article sets out the classic Paretian theory of income distribution. As it does so, it seeks to highlight the constant elements in the human faculties represented, at aggregate level, by the invariability and persistence of the asymmetric income curve, and the variable elements connected with the same curve and manifest in upward and downward mobility – what Pareto calls ‘circulation’. The two theorems arising from Pareto's discovery constitute a specific theory of development which has been confirmed from two points of view: in the positive sense of development when – as in the West – the second theorem has been applied (also independently of Pareto) with the connected theory of the entrepreneur and innovation in democratic regimes; but also in the negative sense of underdevelopment, with the destruction of wealth and the consequent general impoverishment, when expropriation policies have been implemented in despotic regimes, or excessive taxation in others.