Correlation and variability in birth processes

1993 ◽  
Vol 30 (2) ◽  
pp. 275-284 ◽  
Author(s):  
Peter Donnelly ◽  
Thomas Kurtz ◽  
Paul Marjoram
Keyword(s):  
Negative Correlation ◽  
Correlation Structure ◽  
Linear Case ◽  
Birth Process ◽  
Correlation Inequality ◽  
Birth Rates ◽  
Birth Processes

Faddy (1990) has conjectured that the variability of a pure birth process is increased, relative to the linear case, if the birth rates are convex and decreased if they are concave. We prove the conjecture by relating variability to the correlation structure of certain more informative versions of the process. A correlation inequality due to Harris (1977) is used to derive the necessary positive and negative correlation results.

Correlation and variability in birth processes

1993 ◽  
Vol 30 (02) ◽  
pp. 275-284
Author(s):  
Peter Donnelly ◽  
Thomas Kurtz ◽  
Paul Marjoram
Keyword(s):  
Negative Correlation ◽  
Correlation Structure ◽  
Linear Case ◽  
Birth Process ◽  
Correlation Inequality ◽  
Birth Rates ◽  
Birth Processes

Faddy (1990) has conjectured that the variability of a pure birth process is increased, relative to the linear case, if the birth rates are convex and decreased if they are concave. We prove the conjecture by relating variability to the correlation structure of certain more informative versions of the process. A correlation inequality due to Harris (1977) is used to derive the necessary positive and negative correlation results.

scholarly journals On variation in birth processes

1990 ◽  
Vol 22 (02) ◽  
pp. 480-483 ◽  
Author(s):  
M. J. Faddy
Keyword(s):  
Piecewise Linear ◽  
Numerical Results ◽  
Linear Case ◽  
Birth Rates ◽  
Birth Processes

Birth processes with piecewise linear birth rates are analysed, and numerical results suggest that, relative to the linear case, convex birth rates increase variability and concave birth rates decrease variability.

scholarly journals On variation in birth processes

1990 ◽  
Vol 22 (2) ◽  
pp. 480-483 ◽  
Author(s):  
M. J. Faddy
Keyword(s):  
Piecewise Linear ◽  
Numerical Results ◽  
Linear Case ◽  
Birth Rates ◽  
Birth Processes

Birth processes with piecewise linear birth rates are analysed, and numerical results suggest that, relative to the linear case, convex birth rates increase variability and concave birth rates decrease variability.

On the identification of continuous-time Markov chains with a given invariant measure

1994 ◽  
Vol 31 (04) ◽  
pp. 897-910
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Continuous Time ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Birth Process ◽  
Continuous Time Markov Chains ◽  
Branching Process With Immigration ◽  
Birth Processes ◽  
Necessary And Sufficient

In [14] a necessary and sufficient condition was obtained for there to exist uniquely a Q-process with a specified invariant measure, under the assumption that Q is a stable, conservative, single-exit matrix. The purpose of this note is to demonstrate that, for an arbitrary stable and conservative q-matrix, the same condition suffices for the existence of a suitable Q-process, but that this process might not be unique. A range of examples is considered, including pure-birth processes, a birth process with catastrophes, birth-death processes and the Markov branching process with immigration.

On the identification of continuous-time Markov chains with a given invariant measure

1994 ◽  
Vol 31 (4) ◽  
pp. 897-910 ◽  
Author(s):  
P. K. Pollett
Keyword(s):  
Invariant Measure ◽  
Continuous Time ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Birth Process ◽  
Continuous Time Markov Chains ◽  
Branching Process With Immigration ◽  
Birth Processes ◽  
Necessary And Sufficient

In [14] a necessary and sufficient condition was obtained for there to exist uniquely a Q-process with a specified invariant measure, under the assumption that Q is a stable, conservative, single-exit matrix. The purpose of this note is to demonstrate that, for an arbitrary stable and conservative q-matrix, the same condition suffices for the existence of a suitable Q-process, but that this process might not be unique. A range of examples is considered, including pure-birth processes, a birth process with catastrophes, birth-death processes and the Markov branching process with immigration.

Domestic Integration and Suicide in the Provinces of Canada

Crisis ◽  
1999 ◽  
Vol 20 (2) ◽  
pp. 59-63 ◽  
Author(s):  
Antoon A. Leenaars ◽  
David Lester
Keyword(s):  
Social Factors ◽  
Positive Association ◽  
Negative Association ◽  
Birth Rates ◽  
Marriage Rates ◽  
Suicide Rates ◽  
The Social ◽  
Divorce Rates ◽  
Low Levels ◽  
Over Time

Canada's rate of suicide varies from province to province. The classical theory of suicide, which attempts to explain the social suicide rate, stems from Durkheim, who argued that low levels of social integration and regulation are associated with high rates of suicide. The present study explored whether social factors (divorce, marriage, and birth rates) do in fact predict suicide rates over time for each province (period studied: 1950-1990). The results showed a positive association between divorce rates and suicide rates, and a negative association between birth rates and suicide rates. Marriage rates showed no consistent association, an anomaly as compared to research from other nations.

Testing the Assumption of Uncorrelated Errors for Short Scales by Means of Structural Equation Modeling

2014 ◽  
Vol 35 (4) ◽  
pp. 201-211 ◽  
Author(s):  
André Beauducel ◽  
Anja Leue
Keyword(s):  
Structural Equation Modeling ◽  
Negative Correlation ◽  
Structural Equation ◽  
Error Score ◽  
Classical Test Theory ◽  
Test Theory ◽  
Equation Modeling ◽  
Eysenck Personality Questionnaire ◽  
Personality Questionnaire ◽  
True Score

It is shown that a minimal assumption should be added to the assumptions of Classical Test Theory (CTT) in order to have positive inter-item correlations, which are regarded as a basis for the aggregation of items. Moreover, it is shown that the assumption of zero correlations between the error score estimates is substantially violated in the population of individuals when the number of items is small. Instead, a negative correlation between error score estimates occurs. The reason for the negative correlation is that the error score estimates for different items of a scale are based on insufficient true score estimates when the number of items is small. A test of the assumption of uncorrelated error score estimates by means of structural equation modeling (SEM) is proposed that takes this effect into account. The SEM-based procedure is demonstrated by means of empirical examples based on the Edinburgh Handedness Inventory and the Eysenck Personality Questionnaire-Revised.

Hispanic Teen Pregnancy and Birth Rates: Looking Behind the Numbers

2005 ◽  
Author(s):  
Suzanne Ryan ◽  
◽  
Kerry Franzetta ◽  
Jennifer Manlove
Keyword(s):  
Teen Pregnancy ◽  
Birth Rates ◽  
Pregnancy And Birth
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