platykurtic การใช้

• Large values of p and q yield a distribution that is more platykurtic.
• GAMLSS is especially suited for modelling a leptokurtic or platykurtic and / or positively or negatively skewed response variable.
• If the distribution is more peaked than the normal distribution it is said to be leptokurtic; if less peaked it is said to be platykurtic.
• Note that in these cases the platykurtic densities have bounded support, whereas the densities with positive or zero excess kurtosis are supported on the whole real line.
• An example of a platykurtic distribution is the excess kurtosis "', which is the kurtosis minus 3, to provide the comparison to the normal distribution.
• Distributions with kurtosis less than 3 are said to be " platykurtic ", although this does not imply the distribution is " flat-topped " as sometimes reported.
• However, with clean data or in theoretical settings, they can sometimes prove very good estimators, particularly for platykurtic distributions, where for small data sets the mid-range is the most efficient estimator.
• If a distribution has heavy tails, the kurtosis will be high ( sometimes called leptokurtic ); conversely, light-tailed distributions ( for example, bounded distributions such as the uniform ) have low kurtosis ( sometimes called platykurtic ).
• Despite its drawbacks, in some cases it is useful : the midrange is a highly efficient estimator of ?, given a small sample of a sufficiently platykurtic distribution, but it is inefficient for mesokurtic distributions, such as the normal.
• For small sample sizes ( " n " from 4 to 20 ) drawn from a sufficiently platykurtic distribution ( negative excess kurtosis, defined as ? 2 = ( ? 4 / ( ? 2 ) ?) & minus; 3 ), the mid-range is an efficient estimator of the mean " ? ".
• Thus for platykurtic distributions, which can often be thought of as between a uniform distribution and a normal distribution, the informativeness of the middle sample points versus the extrema values varies from " equal " for normal to " uninformative " for uniform, and for different distributions, one or the other ( or some combination thereof ) may be most efficient.