On the mean and varliance of a certain conditional distribution when the underlying distribution is multivariate normal

1975 ◽  
Vol 4 (12) ◽  
pp. 1161-1166
Author(s):  
Dallas W. Anderson
Keyword(s):  
Conditional Distribution ◽  
Multivariate Normal ◽  
Underlying Distribution ◽  
The Mean

scholarly journals COUNT AND DURATION TIME SERIES WITH EQUAL CONDITIONAL STOCHASTIC AND MEAN ORDERS

2020 ◽  
pp. 1-33
Author(s):  
Abdelhakim Aknouche ◽  
Christian Francq
Keyword(s):  
Time Series ◽  
Conditional Distribution ◽  
Stochastic Orders ◽  
Conditional Mean ◽  
Contraction Condition ◽  
Mixing Coefficients ◽  
The Mean ◽  
Quasi Maximum Likelihood ◽  
Geometric Decay ◽  
Mean Function

We consider a positive-valued time series whose conditional distribution has a time-varying mean, which may depend on exogenous variables. The main applications concern count or duration data. Under a contraction condition on the mean function, it is shown that stationarity and ergodicity hold when the mean and stochastic orders of the conditional distribution are the same. The latter condition holds for the exponential family parametrized by the mean, but also for many other distributions. We also provide conditions for the existence of marginal moments and for the geometric decay of the beta-mixing coefficients. We give conditions for consistency and asymptotic normality of the Exponential Quasi-Maximum Likelihood Estimator of the conditional mean parameters. Simulation experiments and illustrations on series of stock market volumes and of greenhouse gas concentrations show that the multiplicative-error form of usual duration models deserves to be relaxed, as allowed in this paper.

On Sequential Procedures for the Point Estimation of the Mean Vector

1988 ◽  
Vol 37 (1-2) ◽  
pp. 47-54 ◽  
Author(s):  
R. Karan Singh ◽  
Ajit Chaturvedi
Keyword(s):  
Normal Population ◽  
Stopping Time ◽  
Point Estimation ◽  
Multivariate Normal ◽  
Minimum Risk ◽  
Sequential Procedures ◽  
Multivariate Normal Population ◽  
Bounded Risk ◽  
The Mean ◽  
Mean Vector

Sequential procedures are proposed for (a) the minimum risk point estimation and (b) the bounded risk point estimation of the mean vector of a multivariate normal population . Second-order approximations are derived. For the problem (b), a lower bound for the number of additional observations (after stopping time) is obtained which ensures “ exact” boundedness of the risk associated witb the sequential procedure.

scholarly journals Uncorrelated genetic drift of gene frequencies and linkage disequilibrium in some models of linked overdominant polymorphisms

1974 ◽  
Vol 24 (3) ◽  
pp. 281-294 ◽  
Author(s):  
Joseph Felsenstein
Keyword(s):  
Linkage Disequilibrium ◽  
Covariance Matrix ◽  
Genetic Drift ◽  
Conditional Distribution ◽  
Large Population ◽  
Multivariate Normal ◽  
Gene Frequencies ◽  
Constant Variance ◽  
Population Sizes ◽  
Multiplicative Family

SUMMARYFor large population sizes, gene frequencies p and q at two linked over-dominant loci and the linkage disequilibrium parameter D will remain close to their equilibrium values. We can treat selection and recombination as approximately linear forces on p, q and D, and we can treat genetic drift as a multivariate normal perturbation with constant variance-covariance matrix. For the additive-multiplicative family of two-locus models, p, q and D are shown to be (approximately) uncorrelated. Expressions for their variances are obtained. When selection coefficients are small the variances of p and q are those previously given by Robertson for a single locus. For small recombination fractions the variance of D is that obtained for neutral loci by Ohta & Kimura. For larger recombination fractions the result differs from theirs, so that for unlinked loci r2 ≃ 2/(3N) instead of 1/(2N). For the Lewontin-Kojima and Bodmer symmetric viability models, and for a model symmetric at only one of the loci, a more exact argument is possible. In the asymptotic conditional distribution in these cases, various of p, q and D are uncorrelated, depending on the type of symmetiy in the model.

Survival of Listeria monocytogenes Strain H7762 and Resistance to Simulated Gastric Fluid following Exposure to Frankfurter Exudate†

2004 ◽  
Vol 67 (6) ◽  
pp. 1170-1176 ◽  
Author(s):  
LAURA D. WONDERLING ◽  
DARRELL O. BAYLES
Keyword(s):  
Listeria Monocytogenes ◽  
Brain Heart Infusion ◽  
Gastric Fluid ◽  
Simulated Gastric Fluid ◽  
Time Of Death ◽  
Nonlinear Regression Analysis ◽  
Underlying Distribution ◽  
Acid Sensitivity ◽  
The Mean ◽  
Mean Time

Listeria monocytogenes strain H7762, a frankfurter isolate, was tested to determine whether it was able to survive at 4°C in frankfurter pack fluid (exudate) and to determine whether food exposure affects its acid sensitivity. Cultures were sampled and tested for acid sensitivity by challenge with simulated gastric fluid (SGF). SGF challenges performed immediately after inoculation revealed that between 20 and 26% of the cells survived the full 30 min of SGF challenge regardless of whether the cells were inoculated into brain heart infusion broth (BHI) or exudate. After 2 days of incubation, cells exposed to both exudate and BHI had significantly decreased SGF resistance; however, the cells exposed to exudate were significantly more SGF resistant than cells exposed to BHI (after 15 min of SGF treatment, 33% of the exudate-exposed cells survived and 12% of the BHI-exposed cells survived). L. monocytogenes exposed to exudate had greater SGF resistance at all challenge times compared with BHI-exposed cells from day 2 through day 4. From days 8 to 15, exudate-exposed cells continued to have greater SGF resistance than BHI-exposed cells up to 10 min of SGF challenge but were as sensitive as the BHI-exposed cells at 20 to 30 min of challenge. By day 25, cells exposed to exudate were significantly more sensitive to SGF challenge than BHI-exposed cells. The survivor data generated from SGF challenges were modeled by a nonlinear regression analysis to calculate the underlying distribution of SGF resistance found in the challenged populations. These analyses indicated that L. monocytogenes exposed to exudate at 48C had a broader distribution of resistance to SGF compared with cells exposed to BHI at 4°C. In addition, the mean time of death during SGF treatment was greater after exposure to exudate, indicating that cells exposed to exudate were more resistant to killing by SGF. These data suggest that exposure to frankfurter exudate might render L. monocytogenes more able to survive the stomach environment during the initial stages of infection.

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