Abstract
The profile likelihood of the reliability parameter θ = P(X < Y) or of the ratio of means, when X and Y are independent exponential random variables, has a simple analytical expression and is a powerful tool for making inferences. Inferences about θ can be given in terms of likelihood-confidence intervals with a simple algebraic structure even for small and unequal samples. The case of right censored data can also be handled in a simple way. This is in marked contrast with the complicated expressions that depend on cumbersome numerical calculations of multidimensional integrals required to obtain asymptotic confidence intervals that have been traditionally presented in scientific literature.
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Díaz-Francés, E., Montoya, J.A. The simplicity of likelihood based inferences for P(X < Y) and for the ratio of means in the exponential model. Stat Papers 54, 499–522 (2013). https://doi.org/10.1007/s00362-012-0446-1
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DOI: https://doi.org/10.1007/s00362-012-0446-1
Keywords
- Comparison of exponential distributions
- Exponential right censored data
- Exponential stress–strength models
- Profile likelihood of reliability parameter
- ROC curves