M. C. Jones
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View article: On mixture relationships between central and non-central chi-squared difference distributions
On mixture relationships between central and non-central chi-squared difference distributions Open
View article: The eschewed sinh-arcsinh <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si62.svg" display="inline" id="d1e973"> <mml:mi>t</mml:mi> </mml:math> distribution
The eschewed sinh-arcsinh distribution Open
View article: Traffic count data analysis using mixtures of Kato–Jones distributions
Traffic count data analysis using mixtures of Kato–Jones distributions Open
We discuss the modelling of traffic count data that show the variation of traffic volume within a day. For the modelling, we apply mixtures of Kato–Jones distributions in which each component is unimodal and affords a wide range of skewnes…
View article: On absolute moment-based upper bounds for L-moments
On absolute moment-based upper bounds for L-moments Open
View article: Duals of convolution thinned relationships
Duals of convolution thinned relationships Open
In a recent article, J. Peyhardi gives a number of novel results related to quasi Pólya thinning which encompass a number of important mixture relationships between univariate discrete distributions. In this note, I explore the duals of th…
View article: A slew of mixture relationships involving discrete and continuous generalized hypergeometric distributions and their special cases
A slew of mixture relationships involving discrete and continuous generalized hypergeometric distributions and their special cases Open
Our starting point is recognition of some mixture relationships involving the (continuous) Gauss hypergeometric distribution. Our main emphasis is then to generalize these relationships to ones involving (discrete) generalized hypergeometr…
View article: Duals of multiplicative relationships involving beta and gamma random variables
Duals of multiplicative relationships involving beta and gamma random variables Open
View article: Uniform and α-Monotone Discrete Distributions
Uniform and α-Monotone Discrete Distributions Open
In this partly expository article, I am concerned with some simple yet fundamental aspects of discrete distributions that are either uniform or have α-monotone probability mass functions. In the univariate case, building on work of F.W. St…
View article: Tractable circula densities from Fourier series
Tractable circula densities from Fourier series Open
View article: A (non‐central) chi‐squared mixture of non‐central chi‐squareds is (non‐central) chi‐squared and related results, corollaries and applications
A (non‐central) chi‐squared mixture of non‐central chi‐squareds is (non‐central) chi‐squared and related results, corollaries and applications Open
Our main, novel, result is that a certain non‐central chi‐squared mixture of non‐central chi‐squared distributions is itself a scaled non‐central chi‐squared distribution. From this and a link to a known result on a mixture representation …
View article: On the ‘optimal’ density power divergence tuning parameter
On the ‘optimal’ density power divergence tuning parameter Open
The density power divergence, indexed by a single tuning parameter α, has proved to be a very useful tool in minimum distance inference. The family of density power divergences provides a generalized estimation scheme which includes…
View article: A Flexible Parametric Modelling Framework for Survival Analysis
A Flexible Parametric Modelling Framework for Survival Analysis Open
Summary We introduce a general, flexible, parametric survival modelling framework which encompasses key shapes of hazard functions (constant; increasing; decreasing; up then down; down then up) and various common survival distributions (lo…
View article: The Cauchy–Schlömilch transformation
The Cauchy–Schlömilch transformation Open
The Cauchy-Schlömilch transformation states that for a function $f$ and $a, \, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the interval $[0, \infty)$ are the same. This elementary result is used to evaluate many non-e…
View article: A Bivariate Power Generalized Weibull Distribution: a Flexible Parametric Model for Survival Analysis
A Bivariate Power Generalized Weibull Distribution: a Flexible Parametric Model for Survival Analysis Open
We are concerned with the flexible parametric analysis of bivariate survival data. Elsewhere, we have extolled the virtues of the "power generalized Weibull" (PGW) distribution as an attractive vehicle for univariate parametric survival an…
View article: Log-location-scale-log-concave distributions for survival and reliability analysis
Log-location-scale-log-concave distributions for survival and reliability analysis Open
We consider a novel sub-class of log-location-scale models for survival and reliability data formed by restricting the density of the underlying location-scale distribution to be log-concave. These models display a number of attractive pro…