Estimation of the probability content in a specified interval using fiducial approach

Ngan Hoang-Nguyen-Thuy and K. Krishnamoorthy

Journal of Applied Statistics, 2021, vol. 48, issue 9, 1541-1558

Abstract: Statistical methods for constructing confidence intervals for the probability content in a specified interval are proposed. Exact and approximate solutions based on the fiducial approach are described when the measurements on the variable of interest can be modelled by a location-scale (or log-location-scale) distribution. Methods are described for the normal, Weibull, two-parameter exponential and two-parameter Rayleigh distributions. For each case, the solutions are evaluated for their merits. Three examples, where it is desired to estimate the percentages of engineering products meet the specification limits, are provided to illustrate the methods.

Date: 2021
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DOI: 10.1080/02664763.2020.1768228

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