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A sub-exponential Weibull random variable may be expressed as a quotient of a unit exponential to an independent strictly positive stable random variable. Based on this property, we propose a test for exponentiality which is consistent against Weibull and Gamma distributions with shape parameter less than unity. A comparison with other procedures is also included.
In the paper a test of the hypothesis , on parameters of the normal distribution is presented, and explicit formulas for critical regions are derived for finite sample sizes. Asymptotic null distribution of the test statistic is investigated under the assumption, that the true distribution possesses the fourth moment.
In this paper, we address the problem of testing hypotheses
using maximum likelihood statistics in non identifiable models.
We derive the asymptotic distribution under very general assumptions.
The key idea is a local reparameterization, depending on the underlying
distribution, which is called locally conic. This method enlights how
the general model induces the structure of the limiting distribution
in terms of dimensionality of some derivative space. We present various
applications of...
This paper shows the statistics that define the likelihood ratio tests about the mean of a k-dimensional normal population, when the hypotheses to test are H0: θ = 0; H0*: θ ∈ τφ; H1: θ ∈ τ; H2: θ ∈ Rk, being τ a closed and poliedric convex cone in Rk, and τφ the minima dimension face in τ.It is proved that the obtained statistics distributions are certain combinations of chi-squared distributions, when θ = 0.At last, it is proved that the power functions of the tests satisfy some desirable properties....
This paper deals with the likelihood ratio test (LRT) for testing hypotheses
on the mixing
measure in mixture models with or without
structural parameter. The main result gives the asymptotic distribution of the LRT
statistics
under some conditions that are proved to be almost necessary.
A detailed solution is given for two testing problems: the
test of a single distribution against any mixture, with application to Gaussian, Poisson and
binomial distributions; the test of the number of populations...
We study the LRT statistic for testing
a single population i.i.d. model against a mixture of two populations with Markov regime.
We prove that
the LRT statistic converges to infinity in probability
as the number of observations tends to infinity.
This is a consequence of a convergence result
of the LRT statistic for a subproblem where the parameters
are restricted to a subset of the whole parameter set.
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