On a Model for Hazard Rates

Abstract

AbutractThis note propOsee a new model for summarising data on survival distribution. A simple graphical method (or equivalently a linear-regression-based method) for estimation of parameters is given. The model is shown to describe adequately data on Survivorship of Starling Birds reported by LACK (1943) and data on power generators reported by DHILLON (1981). A comment is added toillustrate how one can obtain a goodness of fit statistic which has a chi-squared distributions.

A simple test of exponentiality against NWBUE family of life distributions

“…If the ageing profile of a unit is studied through its failure rate function, then a typical approach to modelling non-monotonic ageing is through bathtub failure rate (BFR) models. There is a large body of literature dealing with BFR distributions, see for example References [1][2][3][4][5][6]. Another approach to model non-monotonic ageing uses the notion of mean residual life (MRL) function.…”

Modelling Non-Monotonic Survivorship Data With Bathtub Distributions

“…Double exponential power model. This was proposed by Paranjpe et al (1985), mainly to explain an infant mortality rate that may be higher than the one given by the Smith-Bain model (see Table 1, data for Robins, Starlings, and Herring Gulls). Its hazard function is given by…”

“…Smith and Bain (1975) discuss the statistical analysis of ungrouped data (or a complete data set). Paranjpe et al (1985) discuss methods for grouped data (i.e., data in the form of a life table). Double exponential power model.…”

On non-monotonic ageing properties from the Laplace transform, with actuarial applications

“…Other authors (see, for example, Paranjpe et al (1985)) proposed some parametric models to represent BFR distributions. Aarset (1987) established a test statistic based on the total time on the test plot for testing constant versus bathtub failure rates.…”