Quantile Function Models

  • N. Unnikrishnan Nair
  • P. G. Sankaran
  • N. Balakrishnan
Part of the Statistics for Industry and Technology book series (SIT)


One of the objectives of quantile-based reliability analysis is to make use of quantile functions as models in lifetime data analysis. Accordingly, in this chapter, we discuss the characteristics of certain quantile functions known in the literature. The models considered are the generalized lambda distribution of Ramberg and Schmeiser, the generalized Tukey lambda family of Freimer, Kollia, Mudholkar and Lin, the four-parameter distribution of van Staden and Loots, the five-parameter lambda family and the power-Pareto model of Gilchrist, the Govindarajulu distribution and the generalized Weibull family of Mudholkar and Kollia.

The shapes of the different systems and their descriptive measures of location, dispersion, skewness and kurtosis in terms of conventional moments, L-moments and percentiles are provided. Various methods of estimation based on moments, percentiles, L-moments, least squares and maximum likelihood are reviewed. Also included are the starship method, the discretized approach specifically introduced for the estimation of parameters in the quantile functions and details of the packages and tables that facilitate the estimation process.

In analysing the reliability aspects, one also needs various functions that describe the ageing phenomenon. The expressions for the hazard quantile function, mean residual quantile function, variance residual quantile function, percentile residual life function and their counter parts in reversed time given in the preceding chapters provide the necessary tools in this direction. Some characterization theorems show the relationships between reliability functions unique to various distributions. Applications of selected models and the estimation procedures are also demonstrated by fitting them to some data on failure times.


Failure Time Quantile Function Lifetime Data Reliability Function Life Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • N. Unnikrishnan Nair
    • 1
  • P. G. Sankaran
    • 1
  • N. Balakrishnan
    • 2
  1. 1.Department of StatisticsCochin University of Science and TechnologyCochinIndia
  2. 2.Department of Mathematics and StatisticsMcMasters UniversityHamiltonCanada

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