### Interval Estimate of the Threshold and the Poverty Rate by the Methods of the Simulation

Boudjelal Boukaabar, Mohamed Kheireddine Dellil

#### Abstract

So far, the work and research on the evaluation of the threshold and the poverty rate were satisfied with obtaining a point estimator of these parameters. This assessment is obtained always from a sample of the population whose parameters are under study. In Statistics, such an approach raises the issue of confidence which may be linked to estimators from a sample and used in place of the unknown population parameters. Statisticians rightly consider that no confidence can be given to the point estimators and propose instead using interval estimates. A problem arises if one was to calculate confidence intervals for the parameters that are the poverty threshold and rate: the data. We need a fairly large number of samples from which we calculate the estimators for both parameters. It is only then that we can make a thorough statistical study to estimate confidence intervals for each of the two unknown parameters. Although theoretically this approach does not suffer from any criticism by statisticians, it could prove costly since it requires taking several samples. Moreover, it could be simply unenforceable because requiring probing a large number of individuals to uncover their financial situation. In some societies, it is seen to be awkward to reveal one’s income. Such mentality is current in the Algerian society. This paper proposes a new methodology that solves the problem of the data requirement. This methodology uses the theory of simulation and has the advantage of requiring taking only a single sample. From this base sample we derive the laws of probability needed for the generation of several samples by a computer simulation. Each resulting sample will be used to compute the poverty threshold and the poverty rate attached to it. The collection of these estimators will be used for statistical analysis to evaluate a confidence interval for the threshold and the poverty rate of the original population from which the sample was taken.

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DOI: http://dx.doi.org/10.5539/ibr.v5n10p212

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