Prof.  Amar  Aissani
Universit´e des Sciences et de la Technologie Houari Boumediene,  Algeria

Title: On  Non Parametric Probability Distributions: Probabilistic and Statistical Aspects

Abstract:

Usual probability distributions are "parametric" in the sense that they depend on some parameters. For example, the exponential distribution depends on only one parameter (mean or failure rate); the normal distribution depends on two parameters (mean and variance). However, we can show examples in which the chi-square test leads to accept two different distributions, Gamma and Raighley, which are both characterized by Increasing Failure Rate (IFR).

Indeed, in practice, an engineer is not always interested by the concrete parametric probability distribution itself, but simply in some "aging property" of the system. The more simplest example is given by Reliability or Survival analysis studies , in which practitioners are interested only in a stage of aging or rejuvenation; for example "Increasing(Decreasing) Failure Rate" i.e. IFR(DFR). So, we consider the class of all probability distributions with IFR(DFR)property.Because it contains a collection of probability distributions that share a common aging property, such a class is non-parametric rather than parametric. Other stochastic models, such as queueing , insurance, medicine, or biological models, are also interested in the properties of such classes. In this communication, we will illustrate probabilistic and statistical aspects of such on Non Parametric PDFs on two particular distributions: NBUAFR (New Better than Used Average Failure Rate) and DURL (Decreasing Uncertainty Residual Life) distributions.  Numerical Illustrations will be given in Reliability Analysis on electronical systems and also on Survival Analysis in Medicine and Biological systems. 

Biography: