Continuous or discrete variable: Difference between revisions

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==Mixture of continuous and discrete variables==

A mixed multivariate model containscan contain 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>