This paper introduces a transmuted generalized inverted exponential distribution. We generalize the two parameter generalized inverted exponential distribution using the quadratic rank transmutation map proposed by Shaw et al. (2007) to develop a transmuted generalized inverted exponential...

The stress-strength reliability <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$R=P(YX)$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$X$$</EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$Y$$</EquationSource> </InlineEquation> are independent continuous random variables, has obtained wide attention in many areas of application, such as in engineering statistics and biostatistics. Classical likelihood-based inference about <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$R$$</EquationSource> </InlineEquation> has been widely...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

For a system with i.i.d. component lifetimes the Samaniego signature can be computed for instance from Boland’s formula, which requires the knowledge of every value of the associated structure function. We show how the signature can be computed more efficiently from the diagonal section of the...

The subsignatures of a system with continuous and exchangeable component lifetimes form a class of indexes ranging from the Samaniego signature to the Barlow–Proschan importance index. These indexes can be computed through explicit linear expressions involving the values of the structure...

The Uniformly Minimum Variance Unbiased (UMVU) and the Maximum Likelihood (ML) estimations of R = P(X È Y) and the associated variance are considered for independent discrete random variables X and Y. Assuming a discrete uniform distribution for X and the distribution of Y as a member of the...