Fixed Point Iteration for Estimating The Parameters of Extreme Value Distributions

Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which requires differentiation unlike the fixed point iteration which is also easier to implement. Graphical approaches are also usually proposed in the literature. We prove that these reduce in fact to the fixed point solution proposed in this paper

Measuring inequality: application of semi-parametric methods to real life data

A number of methods have been introduced in order to measure the inequality in various situations such as income and expenditure. In order to curry out statistical inference, one often needs to estimate the available measures of inequality. Many estimators are available in the literature, the most used ones being the non parametric estimators. kpanzou(2011) has developed semi-parametric estimators for measures of inequality and showed that these are very appropriate especially for heavy tailed distributions. In this paper we apply such semi-parametric methods to a practical data set and show how they compare to the non parametric estimators. A guidance is also given on the choice of parametric distributions to fit in the tails of the dataComment: 1

A result on the bias of sieve profile estimators

We show how to control the bias of a sieve type profile estimator under natural conditions on the Hessian of the expected contrast functional

Interval Estimation of the Unknown Exponential Parameter Based on Time Truncated Data

In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid censoring cases. All the results available today are based on the conditional argument that at least one failure occurs during the experiment. In this paper we provide some inferential results based on the unconditional argument. We extend the results for some two-parameter distributions also

Parameter estimation of beta-geometric model with application to human fecundability data

The present study deals with the estimation of the mean value of fecundability by fitting a theoretical distribution from the observed month of first conception of the married women who did not use any contraceptive method before their first conception. It is assumed that fecundability is fixed for a given couple, but across couples it varies according to a specified distribution. Under the classical approach, methods of moment and maximum likelihood are used while for Bayesian approach we use the above two estimates as prior for fecundability parameter. A real data analysis from the third National Family Health Survey (NFHS-III) is analyzed as an application of model. Finally, a simulation study is performed to access the performance of the several of methods used in this pape

Order preserving property of moment estimators

Balakrishnan and Mi [1] considered order preserving property of maximum likelihood estimators. In this paper there are given conditions under which the moment estimators have the property of preserving stochastic orders. There is considered property of preserving for usual stochastic order as well as for likelihood ratio order. Mainly, sufficient conditions are given for one parameter family of distributions and also for exponential family, location family and scale family

On the structure of UMVUEs

In all setups when the structure of UMVUEs is known, there exists a subalgebra $\cal U$ (MVE-algebra) of the basic $\sigma$-algebra such that all $\cal U$-measurable statistics with finite second moments are UMVUEs. It is shown that MVE-algebras are, in a sense, similar to the subalgebras generated by complete sufficient statistics. Examples are given when these subalgebras differ, in these cases a new statistical structure arises.Comment: Accepted for publication in Sankhya

An iterative tomogravity algorithm for the estimation of network traffic

This paper introduces an iterative tomogravity algorithm for the estimation of a network traffic matrix based on one snapshot observation of the link loads in the network. The proposed method does not require complete observation of the total load on individual edge links or proper tuning of a penalty parameter as existing methods do. Numerical results are presented to demonstrate that the iterative tomogravity method controls the estimation error well when the link data is fully observed and produces robust results with moderate amount of missing link data.Comment: Published at http://dx.doi.org/10.1214/074921707000000030 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Log-Lindley generated family of distributions

A new generator of univariate continuous distributions, with two additional parameters, called the Log-Lindley generated family is introduced. Some special distributions in the new family are presented. Some mathematical properties of the new family are studied. The maximum likelihood method to estimate model parameters is employed. The potentiality of the new generator is illustrated using a real data set

A characterization of best unbiased estimators

A simple characterization of uniformly minimum variance unbiased estimators (UMVUEs) is provided (in the case when the sample space is finite) in terms of a linear independence condition on the likelihood functions corresponding to the possible samples. The crucial observation in the proof is that, if a UMVUE exists, then, after an appropriate cleaning of the parameter space, the nonzero likelihood functions are eigenvectors of an "artificial" matrix of Lagrange multipliers, and the values of the UMVUE are eigenvalues of that matrix. The characterization is then extended to best unbiased estimators with respect to arbitrary convex loss functions.Comment: 4 pages. Version 2: the paper is thoroughly reworked, even the title and the abstract have changed; the method remains the same. Version 3: a corollary, a proposition, and two examples (on Bernoulli and Beta-Bernoulli trials) are added; two typos are fixe