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In [[discrete time]] dynamics, the variable ''time'' is treated as discrete, and the equation of evolution of some variable over time is called a [[difference equation]].
In [[econometrics]] and more generally in [[regression analysis]], sometimes some of the variables being [[empirical]]ly related to each other are 0-1 variables, being permitted to take on only those two values.<ref>{{cite journal |last1=Miller |first1=Jerry L.L. |last2=Erickson |first2=Maynard L. |title=On Dummy Variable Regression Analysis |journal=Sociological Methods & Research |date=May 1974 |volume=2 |issue=4 |page=395-519 |doi=10.1177/004912417400200402}}</ref> The purpose of the discrete values of 0 and 1 is to use the dummy variable as a ‘switch’ that can ‘turn on’ and ‘turn off’ by assigning the two values to different parameters in an equation. A variable of this type is called a [[dummy variable (statistics)|dummy variable]]. If the [[dependent variable]] is a dummy variable, then [[logistic regression]] or [[probit regression]] is commonly employed. In the case of regression analysis, a dummy variable can be used to represent subgroups of the sample in a study (e.g. the value 0 corresponding to a constituent of the control group). <ref>{{cite book |last1=Hardy |first1=Melissa A. |title=Regression with Dummy Variables (Quantitative Applications in the Social Sciences) |date=February 25, 1993 |publisher=Sage Publications, Inc. |___location=Newbury Park |isbn=0803951280 |page=v |edition=1st}}</ref>
==Mixture of discrete and continuous variables==
A mixed multivariate model contains both discrete and continuous variables. For instance, a simple mixed multivariate model could have a discrete variable <math>x</math>, which only takes on values 0 or 1, and a continuous variable <math>y</math>.<ref>{{cite journal |last1=Olkin |first1=Ingram |last2=Tate |first2=Robert |title=Multivariate Correlation Models with Mixed Discrete and Continuous Variables |journal=The Annals of Mathematical Statistics |date=June 1961 |volume=32 |issue=2 |page=448-465 |doi=10.1214/aoms/1177705052}}</ref> An example of a mixed model could be a research study on the risk of psychological disorders based on one binary measure of psychiatric symptoms and one continuous measure of cognitive performance.<ref>{{cite journal |last1=Fitzmaurice |first1=Garrett M. |last2=Laird |first2=Nan M. |title=Regression Models for Mixed Discrete and Continuous Responses with Potentially Missing Values |journal=Biometrics |date=March 1997 |volume=53 |issue=1 |page=110-122 |doi=10.2307/2533101}}</ref> Mixed models may also involve a single variable that is discrete over some range of the number line and continuous at another range.
In probability theory and statistics, the probability distribution of a mixed random variable consists of both discrete and continuous components. A mixed random variable does not have a [[Cumulative distribution function|cumulative distribution function]] that is discrete or everywhere-continuous. An example of a mixed type random variable is the probability of wait time in a queue. The likelihood of a customer experiencing a zero wait time is discrete, while non-zero wait times are evaluated on a continuous time scale.<ref>{{cite journal |last1=Sharma |first1=Shalendra D. |title=On a Continuous/Discrete Time Queueing System with Arrivals in Batches of Variable Size and Correlated Departures |journal=Journal of Applied Probability |date=March 1975 |volume=12 |issue=1 |page=115-129 |doi=10.2307/3212413}}</ref>
==See also==
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