154 research outputs found
Exponential families of mixed Poisson distributions
If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq
An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums
By a modification of the method that was applied in (Korolev and Shevtsova,
2009), here the inequalities
and
are proved for the
uniform distance between the standard normal distribution
function and the distribution function of the normalized sum of an
arbitrary number of independent identically distributed random
variables with zero mean, unit variance and finite third absolute moment
. The first of these inequalities sharpens the best known version of
the classical Berry--Esseen inequality since
by virtue of
the condition , and 0.4785 is the best known upper estimate of the
absolute constant in the classical Berry--Esseen inequality. The second
inequality is applied to lowering the upper estimate of the absolute constant
in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051
which is strictly less than the least possible value of the absolute constant
in the classical Berry--Esseen inequality. As a corollary, the estimates of the
rate of convergence in limit theorems for compound mixed Poisson distributions
are refined.Comment: 33 page
A functional approach to estimation of the parameters of generalized negative binomial and gamma distributions
The generalized negative binomial distribution (GNB) is a new flexible family
of discrete distributions that are mixed Poisson laws with the mixing
generalized gamma (GG) distributions. This family of discrete distributions is
very wide and embraces Poisson distributions, negative binomial distributions,
Sichel distributions, Weibull--Poisson distributions and many other types of
distributions supplying descriptive statistics with many flexible models. These
distributions seem to be very promising for the statistical description of many
real phenomena. GG distributions are widely applied in signal and image
processing and other practical problems. The statistical estimation of the
parameters of GNB and GG distributions is quite complicated. To find estimates,
the methods of moments or maximum likelihood can be used as well as two-stage
grid EM-algorithms. The paper presents a methodology based on the search for
the best distribution using the minimization of -distances and
-metrics for GNB and GG distributions, respectively. This approach, first,
allows to obtain parameter estimates without using grid methods and solving
systems of nonlinear equations and, second, yields not point estimates as the
methods of moments or maximum likelihood do, but the estimate for the density
function. In other words, within this approach the set of decisions is not a
Euclidean space, but a functional space.Comment: 13 pages, 6 figures, The XXI International Conference on Distributed
Computer and Communication Networks: Control, Computation, Communications
(DCCN 2018
On finite-time ruin probabilities for classical risk models
info:eu-repo/semantics/publishe
A copula model for marked point processes
The final publication (Diao, Liqun, Richard J. Cook, and Ker-Ai Lee. (2013) A copula model for marked point processes. Lifetime Data Analysis, 19(4): 463-489) is available at Springer via http://dx.doi.org/10.1007/s10985-013-9259-3Many chronic diseases feature recurring clinically important events. In addition, however, there
often exists a random variable which is realized upon the occurrence of each event reflecting the
severity of the event, a cost associated with it, or possibly a short term response indicating the
effect of a therapeutic intervention. We describe a novel model for a marked point process which
incorporates a dependence between continuous marks and the event process through the use of a
copula function. The copula formulation ensures that event times can be modeled by any intensity
function for point processes, and any multivariate model can be specified for the continuous
marks. The relative efficiency of joint versus separate analyses of the event times and the marks is
examined through simulation under random censoring. An application to data from a recent trial
in transfusion medicine is given for illustration.Natural Sciences and Engineering Research Council of Canada (RGPIN 155849); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626
Teaching introductory programming: a quantitative evaluation of different approaches
© ACM, 2014. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Transactions on Computing Education, 2014, Vol. 14, No. 4, Article 26, DOI: http://dx.doi.org/10.1145/266241
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