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A bivariate, multimodal distribution Figure 4. A non-example: a unimodal distribution, that would become multimodal if conditioned on either x or y. In statistics, a multimodal distribution is a probability distribution with more than one mode (i.e., more than one local peak of the distribution).
For example, when studying education a fixed effect could represent overall school level effects that are consistent across all schools. While the hierarchy of the data set is typically obvious, the specific fixed effects that affect the average responses for all subjects must be specified.
The Beta distribution on [0,1], a family of two-parameter distributions with one mode, of which the uniform distribution is a special case, and which is useful in estimating success probabilities. The four-parameter Beta distribution, a straight-forward generalization of the Beta distribution to arbitrary bounded intervals [,].
As an example, the sum of two jointly normally distributed random variables, each with different means, will still have a normal distribution. On the other hand, a mixture density created as a mixture of two normal distributions with different means will have two peaks provided that the two means are far enough apart, showing that this ...
As the examples above show, zero-inflated data can arise as a mixture of two distributions. The first distribution generates zeros. The first distribution generates zeros. The second distribution, which may be a Poisson distribution , a negative binomial distribution or other count distribution, generates counts, some of which may be zeros.
The following is an example of applying a continuity correction. Suppose one wishes to calculate Pr(X ≤ 8) for a binomial random variable X. If Y has a distribution given by the normal approximation, then Pr(X ≤ 8) is approximated by Pr(Y ≤ 8.5). The addition of 0.5 is the continuity correction; the uncorrected normal approximation gives ...
Andy Field (2009) [1] provided an example of a mixed-design ANOVA in which he wants to investigate whether personality or attractiveness is the most important quality for individuals seeking a partner. In his example, there is a speed dating event set up in which there are two sets of what he terms "stooge dates": a set of males and a set of ...
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1] A bimodal distribution would have two high points rather than one. The shape of a distribution is ...