We revisit stochastic thermodynamics for a system with discrete energy states in contact with a heat and particle reservoir.

We study the life distribution of an operating device through the notion of mean residual life. The device is experiencing a random number of shocks governed by a homogeneous Poisson process, and a new U-statistic test procedure is introduced to test the hypothesis of that the life is...

Abstract We consider the Dagum distribution for estimating the reliability of a k -component stress-strength system with different shape values of the shape parameter. We assume that the system has strength modelled by k independent and identically distributed random variables, and each...

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>

We consider the problem of estimating R=P(XY) where X and Y have independent exponential distributions with parameters θ and λ respectively and a common location parameter μ. Assuming that there is a prior guess or estimate R <Subscript>0</Subscript>, we develop various shrinkage estimators of R that incorporate...</subscript>

We introduce a weighted-moving-average analysis for the tick-by-tick data of yen–dollar exchange rates. The weights are determined automatically for given data by applying the Yule–Walker formula for autoregressive model. Although the data are non-stationary, the resulting moving average...