We show that, for discrete exponential families, the sample mean of n observations does not stochastically dominate a single observation when estimating the population mean. This is in stark contrast to the case of a normal distribution.

Based on a record sample from the Rayleigh model, we consider the problem of estimating the scale and location parameters of the model and predicting the future unobserved record data. Maximum likelihood and Bayesian approaches under different loss functions are used to estimate the model's...

Based on a record sample from the Rayleigh model, we consider the problem of estimating the scale and location parameters of the model and predicting the future unobserved record data. Maximum likelihood and Bayesian approaches under different loss functions are used to estimate the model's...

The Shannon entropy of a random variable has become a very useful tool in Probability Theory. In this paper we extend the concept of cumulative residual entropy introduced by Rao et al. (in IEEE Trans Inf Theory 50:1220–1228, <CitationRef CitationID="CR13">2004</CitationRef>). The new concept called generalized cumulative residual...</citationref>

In this paper some different sorts of confidence intervals are considered for the scale parameter of the Burr type XII distribution based on the upper record values. In this regard, the coverage probability is adopted as a measure of improvement when the endpoints are the same for all types of...

In this paper, maximum likelihood and Bayesian approaches have been used to obtain the estimation of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$P(XY)$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>P</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo></mo> <mi>Y</mi> <mo stretchy="false">)</mo> </mrow> </math> </EquationSource> </InlineEquation> based on a set of upper record values from Kumaraswamy distribution. The existence and uniqueness of the maximum likelihood estimates of the Kumaraswamy distribution...</equationsource></equationsource></inlineequation>