Joint confidence region for the parameters of pareto distribution

The Pareto distribution is commonly used by economists as a model for the distribution of incomes. Separate confidence intervals or approximate confidence intervals for the parameters of Pareto distribution were discussed by some authors. This paper discusses exact joint confidence region for the parameters of Pareto distribution. The method can be used for both complete samples and type II censored samples.     

Thresholds in pareto sets

We use catastrophe theory to discuss the generic ways in which a system determined by the optimization of several real-valued functions, such as a pure exchange economy, can break its stability and make a transition from ‘slow’ to ‘fast’ movement.     

Bayesian inference for pareto populations

Bayesian techniques for samples from classical, generalized and multivariate Pareto distributions are described. We place emphasis on choosing proper prior distributions that do not lead to anomalous posterior densities.     

Ruling out pareto dominated monetary equilibria

It is well known that under nominal money supply rules accomplished through lump sum transfers, non-uniqueness and non-optimality of the resource allocation often obtains in monetary models. We show that uniqueness and optimality of the resource allocation obtains if the monetary authority conducts Friedman's rule through open market operations. Our result necessitates and we provide a clarification of existing irrelevance theorems for open market operations. Our result also provides a partial resolution of the uniqueness-efficiency conflict of nominal money supply rules raised by Woodford (Economic Theory 4 (1994) 345–380).     

A note on local pareto optima

This note gives an elementary proof of the sufficient second order conditions for a local Pareto optimum.     

Notes on pareto improvement in incomplete financial markets

these notes describe some recent developments in the analysis of the possibilities for Pareto improvement when, in a competitive environment, financial markets are incomplete. The basic framework is a general methodology for investigating the welfare effects of policy or institutional changes in equilibrium models, when these can be characterized in terms of perturbing the solutions to a system, of smooth equations. Two particular scenarios are discussed in detail: First, the situation where a central government can intervene in the form of wealth taxes and subsidies, and second, the situation where the financial institutions can be modified by increasing the number of available instruments.

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Sommario Queste osservazioni descrivono alcuni sviluppi recenti dell'analisi del miglioramento paretiano quando, in un contesto competitivo, i mercati finanziari sono incompleti. La struttura di riferimento è la metodologia generale per indagare gli effetti sul benessere sociale di cambiamenti politici o istituzionali nei modelli di equilibrio, quando questi possono essere caratterizzati come una perturbazione delle soluzioni di un sistema di equazioni. Due scenari particolari vengono discussi in dettaglio: nel primo, un governo centrale può intervenire attraverso la tassazione sulla ricchezza e le sovvenzioni; nel secondo, le istituzioni finanziarie possono essere modificate mediante l'aumento degli strumenti disponibili.

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While working in this general area I have benefitted substantially from interaction and collaboration with several of my, sometime Penn colleagues or students, Alex Citanna, Atsushi Kajii, Marcos Lisboa and Antonio Villanacci. Conversations at various points with Ronel Elul, John Geanakoplos, Heracles Polemarchakis and especially, Paolo Siconolfi have also been extremely helpful and illuminating. None of them, however, is responsible for my biases and idiosyncrasies. These notes were prepared for a presentation at the AMASES Conference held in Pugnochiuso, Italy during September 25–28, 1995.     

Estimation of the scale parameter of a log-logistic distribution

In this work the ranked set sampling technique has been applied to estimate the scale parameter $\alpha $ of a log-logistic distribution under a situation where the units in a sample can be ordered by judgement method without any error. We have evaluated the Fisher information contained in the order statistics arising from this distribution and observed that median of a random sample contains the maximum information about the parameter $\alpha $ . Accordingly we have used median ranked set sampling to estimate $\alpha $ . We have further carried out the multistage median ranked set sampling to estimate $\alpha $ with improved precision. Suppose it is not possible to rank the units in a sample according to judgement method without error but the units can be ordered based on an auxiliary variable $Z$ such that $(X, Z)$ has a Morgenstern type bivariate log-logistic distribution (MTBLLD). In such a situation we have derived the Fisher information contained in the concomitant of rth order statistic of a random sample of size $n$ from MTBLLD and identified those concomitants among others which possess largest amount of Fisher information and defined an unbalanced ranked set sampling utilizing those units in the sample and thereby proposed an estimator of $\alpha $ using the measurements made on those units in this ranked set sample.     

Estimation of the parameters of log-gamma distribution using order statistics

In this work we propose a technique of estimating the location parameter μ and scale parameter σ of log-gamma distribution by U-statistics constructed by taking best linear functions of order statistics as kernels. The efficiency comparison of the proposed estimators with respect to maximum likelihood estimators is also made.     

Estimation of the parameters of the Weibull distribution for censored samples

The Weibull distribution is an often used model in survival analysis of technical products. In this paper confidence estimations for the parameters of the Weibull distribution are developed for type I censored samples without and with replacements.     

Implementing lifetime performance index for the pareto lifetime businesses of the service industries

Process capability analysis is an effective means of measuring process performance and potential capability. In the service industries, process capability indices (PCIs) are utilized to assess whether business quality meets the required level. Hence, the performance index C _L is used as a means of measuring business performance, where L is the lower specification limit. In the technology of data transformation, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of C _L based on the right type II censored sample from the pareto distribution. The UMVUE of C _L is then utilized to develop a novel hypothesis testing procedure in the condition of known L. Finally, we give one practical example and the Monte Carlo simulation to assess the behavior of this test statistic for testing null hypothesis under given significance level. Moreover, the managers can then employ the new testing procedure to determine whether the business performance adheres to the required level.     

The topological equivalence of the pareto condition and the existence of a dictator

The paper studies two standard properties of rules for aggregating individual into social preferences: non-dictatorship and the Pareto condition. Together with the condition of independence of irrelevant alternatives, these are the three basic axioms of Arrow's social choice paradox.We prove the topological equivalence between the Pareto condition and the existence of a dictator for continuous rules. The axiom of independence of irrelevant alternatives is not required.The results use a topological framework for aggregation introduced in Chichilnisky (1980), but under different conditions. In Chichilnisky (1980) rules are anonymous and respect unanimity. Since anonymity is strictly stronger than the condition of non-dictatorship, while respect of unanimity is strictly weaker than the Pareto condition, the two sets of conditions are not comparable.     

Estimation of the parameter of the inverse Gaussian distribution from generalised censored samples

In this paper, a new Type of censored sample referred as generalised censored sample is defined and is differentiated fromCohen's [1963] progressively censored type I and type II samples. The maximum likelihood estimate of the parameter of the inverse Gaussian distribution from generalised censored samples is obtained. An expression for the standard error of the estimate is given.     

Estimation of the order restricted scale parameters for two populations from the Lomax distribution

The usual methods of estimating the unknown parameters of a distribution, use only the information given from the sample data. In many cases, there is, also, another important information for estimating the unknown parameters of our model, such as the order of these parameters, and this last information improves the quality of estimation. In this paper, we deal with the problem of estimating the ordered scale parameters from two populations of the multivariate Lomax distribution, with unknown location parameters. It is proved that the best equivariant estimators of the scale parameters (in the unrestricted case) are not admissible and we construct estimators that improve upon the usual ones (when these parameters are known to be ordered).     

Walras degrees and probability of a blocking coalition at pareto allocations

We attempt to determine the probability of a blocking coalition from a notion of being non- Walrasian which does not rely on the explicit use of norms. The key concept introduced is that of Walras degrees. Theorem 1 gives the bounds of the probability of blocking in terms of these degrees. Theorem 2 gives the asymptotic conditional probability of a blocking coalition given that coalitions are losing. The relationship between the degrees of the conventional norms on allocations is also investigated.     

Estimation of the parameters in the gravity model for trip distribution : A new method and solution algorithm

For the unique determination of the parameters in the doubly constrained gravity model with exponential friction function two approaches are common: (1) entropy maximization and (2) application of a travel cost budget. This paper shows by making use of geometric programming that both of these approaches are equivalent with another natural criterion: the minimization of the deviation between the observed [t_1j] and the estimated [x_1j] table for a base year. By means of calculating the derivative of total cost as a function of σ the construction of an efficient algorithm for estimation of σ is made possible.