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In many applications, we assume that two random observations x and yare generated according to independent Poisson distributions x1d4ab;(λS) and x1d4ab;(μT) and we are interested in performing statistical inference on the ratio φ = λ / μ of the two incidence rates. In vaccine efficacy trials, x and y are typically the numbers of cases in the vaccine and the control groups respectively, φ is called the relative risk and the statistical model is called ‘partial immunity model’. In this paper we...
In many applications, we assume that two random observations x and
y are generated according to independent Poisson distributions
𝒫(λS)
and 𝒫(μT)
and we are interested in performing statistical inference on the ratio
φ = λ / μ of the two
incidence rates. In vaccine efficacy trials, x and y are
typically the numbers of cases in the vaccine and the control groups respectively,
φ is called the relative risk...
We consider a construction of approximate confidence intervals on the variance component in mixed linear models with two variance components with non-zero degrees of freedom for error. An approximate interval that seems to perform well in such a case, except that it is rather conservative for large was considered by Hartung and Knapp in [hk]. The expression for its asymptotic coverage when suggests a modification of this interval that preserves some nice properties of the original and that...
In this paper, we study the interval estimation for the mean from inverse Gaussian distribution. This distribution is a member of the natural exponential families with cubic variance function. Also, we simulate the coverage probabilities for the confidence intervals considered. The results show that the likelihood ratio interval is the best interval and Wald interval has the poorest performance.
An asymptotic analysis, when the sample size n tends to infinity, of the optimal confidence region established in Czarnowska and Nagaev (2001) is considered. As a result, two confidence regions, both close to the optimal one when n is sufficiently large, are suggested with a mild assumption on the distribution of a location-scale family.
By using three theorems (Oktaba and Kieloch [3]) and Theorem 2.2 (Srivastava and Khatri [4]) three results are given in formulas (2.1), (2.8) and (2.11). They present asymptotically normal confidence intervals for the determinant in the MGM model , , scalar , with a matrix . A known random matrix has the expected value , where the matrix is a known matrix of an experimental design, is an unknown matrix of parameters and is the covariance matrix of being the symbol of the Kronecker...
Confidence intervals and regions for the parameters of a distribution are constructed, following the method due to L. N. Bolshev. This construction method is illustrated with Poisson, exponential, Bernouilli, geometric, normal and other distributions depending on parameters.
2000 Mathematics Subject Classification: 62F25, 62F03.A two-sided conditional confidence interval for the scale parameter θ of a Weibull distribution is constructed. The construction follows the rejection of a preliminary test for the null hypothesis: θ = θ0 where θ0 is a
given value. The confidence bounds are derived according to the method set
forth by Meeks and D’Agostino (1983) and subsequently used by Arabatzis et
al. (1989) in Gaussian models and more recently by Chiou and Han (1994,
1995)...
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