Every abstract type of a belief-closed type space corresponds to an infinite belief hierarchy. But only finite order of beliefs is necessary for most applications. As we demonstrate, many important insights from recent development in the theory of Bayesian games with higher-order uncertainty...

The ISO* property of noncentrality parameters is derived for the expected value of an ISO* function of independent nonnegative two-parameter compound Poisson random variables and is then applied to unbiasedness of tests and monotonicity of power functions of tests in an order-restricted...

The stuttering generalized Waring distribution is introduced and shown to arise through two urn genesis schemes. Its probability generating function and moments are derived and some potential applications are discussed

A new family of compound Poisson distribution functions from quantitative linguistics is used to study the linguistic features of DNA sequences that go beyond the Zipf's law. The relative frequency distribution of n-tuples and the compositional segmentation study can be fit reasonably well using...

A common feature for compound Poisson and Katz distributions is that both families may be viewed as generalizations of the Poisson law. In this paper, we present a unified approach in testing the fit to any distribution belonging to either of these families. The test involves the probability...

The weighted sum <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$S=w_1S_1+w_2S_2+\cdots +w_NS_N$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>S</mi> <mo>=</mo> <msub> <mi>w</mi> <mn>1</mn> </msub> <msub> <mi>S</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>w</mi> <mn>2</mn> </msub> <msub> <mi>S</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msub> <mi>w</mi> <mi>N</mi> </msub> <msub> <mi>S</mi> <mi>N</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation> is approximated by compound Poisson distribution. Here <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$S_i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>S</mi> <mi>i</mi> </msub> </math> </EquationSource> </InlineEquation> are sums of symmetric independent identically distributed discrete random variables, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$w_i$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mi>w</mi> <mi>i</mi> </msub> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>

The compound Poisson INAR(1) model for time series of overdispersed counts is considered. For such CPINAR(1) processes, explicit results are derived for joint moments, for the k-step-ahead distribution as well as for the stationary distribution. It is shown that a CPINAR(1) process is strongly...

Probability generating function (p.g.f.) is a powerful tool to study discrete compound Poisson (DCP) distribution. By applying inverse Fourier transform of p.g.f., it is convenient to numerically calculate probability density and do parameter estimation. As an application to finance and...