1,245 research outputs found
Using epidemic prevalence data to jointly estimate reproduction and removal
This study proposes a nonhomogeneous birth--death model which captures the
dynamics of a directly transmitted infectious disease. Our model accounts for
an important aspect of observed epidemic data in which only symptomatic
infecteds are observed. The nonhomogeneous birth--death process depends on
survival distributions of reproduction and removal, which jointly yield an
estimate of the effective reproduction number as a function of epidemic
time. We employ the Burr distribution family for the survival functions and, as
special cases, proportional rate and accelerated event-time models are also
employed for the parameter estimation procedure. As an example, our model is
applied to an outbreak of avian influenza (H7N7) in the Netherlands, 2003,
confirming that the conditional estimate of declined below unity for the
first time on day 23 since the detection of the index case.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS270 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A Guide to the Dagum Distributions
In a series of papers in the 1970s, Camilo Dagum proposed several variants of a new model for the size distribution of personal income. This Chapter traces the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. It also provides interrelations with other statistical distributions as well as aspects that are of special interest in the income distribution eld, including Lorenz curves and the Lorenz order and inequality measures. The Chapter ends with a survey of empirical applications of the Dagum distributions, many published in Romance language periodicals.
Classes of Ordinary Differential Equations Obtained for the Probability Functions of Burr XII and Pareto Distributions
In this paper, the differential calculus was used
to obtain some classes of ordinary differential equations (ODE)
for the probability density function, quantile function, survival
function, inverse survival function, hazard function and
reversed hazard function of Burr XII and Pareto distributions.
This was made easier since later distribution is a special case of
the former. The stated necessary conditions required for the
existence of the ODEs are consistent with the various
parameters that defined the distributions. Solutions of these
ODEs by using numerous available methods are new ways of
understanding the nature of the probability functions that
characterize the distributions
On The Weighted BurrXII Distribution: Theory and Practice
We take an in-depth look at the weighted Burr-XII distribution. This distribu-tion generalizes Burr-XII, Lomax, and log-logistic distributions. We discuss the dis-tributional characteristics of the probability density function, the failure rate function,and mean residual lifetime of this distribution. Moreover, we obtain various statisti-cal properties of this distribution such as moment generating function, entropies, meandeviations, order statistics and stochastic ordering. The estimation of the distributionparameters via maximum likelihood method and the observed Fisher information ma-trix are discussed. We further employ a simulation study to investigate the behavior ofthe maximum likelihood estimates (MLEs). A test concerning the existence of size-biasin the sample is provided. In the end, a real data is presented and is analyzed usingthis distribution along with some existing distributions for illustrative purposes
Minimum L-distance estimators for non-normalized parametric models
We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, and is to be classified as a minimum distance estimator, incorporating as a distance function the Lânorm. Throughout, we deal rigorously with issues of existence and measurability of these implicitly defined estimators. Moreover, we provide consistency results in a common asymptotic setting, and compare our new method with classical estimators for the exponential, the Rayleigh and the Burr Type XII distribution in Monte Carlo simulation studies. We also assess the performance of different estimators for nonânormalized models in the context of an exponentialâpolynomial family
Minimum -distance estimators for non-normalized parametric models
We propose and investigate a new estimation method for the parameters of
models consisting of smooth density functions on the positive half axis. The
procedure is based on a recently introduced characterization result for the
respective probability distributions, and is to be classified as a minimum
distance estimator, incorporating as a distance function the -norm.
Throughout, we deal rigorously with issues of existence and measurability of
these implicitly defined estimators. Moreover, we provide consistency results
in a common asymptotic setting, and compare our new method with classical
estimators for the exponential-, the Rayleigh-, and the Burr Type XII
distribution in Monte Carlo simulation studies. We also assess the performance
of different estimators for non-normalized models in the context of an
exponential-polynomial family.Comment: 27 pages, 8 table
Weibull, Îș-Weibull and Other Probability Distributions
Here we will consider a function of Îș-statistics, the Îș-Weibull distribution, and compare it to the well-known Weibull distribution. The Îș-Weibull will be also compared to the 3-parameter extended Weibull function, obtained according to the MarshallâOlkin extended distributions. The log-logistic distribution will be considered for comparison too, such as the exponentiated Weibull, the Burr and the q-Weibull distributions. The most important observation, coming from the proposed calculations, is that the Îș-Weibull hazard function is strongly depending on the values of parameter Îș, a parameter which is deeply influencing the behaviour of the tail of the probability distribution. As a consequence, the Îș-Weibull function turns out to be quite relevant for generalizations of the Weibull approach to modeling failure times. Discussions about the Maximum Likelihood approach for Weibull, Îș-Weibull and Burr distributions will be also given
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