In statistics, a random vector of non-normal random variables has been characterized as heteroscedastic when the variation of the random variable is different in different parts of the vector. Here, the variation can be measured by the normal or variance of statistical dispersion or the difference between the means of the sample and the mean of the distribution. Hence, heteroscedasticity is usually referred to as the absence of homogeneous uniformity. It is an important parameter to be considered in studies that are concerned with the behavior of statistical distributions. It is also important in situations where the distributions have a high degree of dispersion, because they may be more complex than those which have a high degree of uniformity.
There are two forms of heteroscedastics, those occurring due to the presence of normal curve and those resulting from the presence of negative correlation. Heteroscedastics in statistical data cannot be avoided because they arise from various causes such as random fluctuations which affect the data, external disturbances, and internal processes.
The most common form of heteroscedastics, which occurs due to the normal curve, is called the zero-distance normality. This happens when a non-normal curve is fitted to a set of independent variables, such as a set of natural log-normals. If one or more of these natural log-normals have zero-distance normality, then the data can be interpreted as having zero correlations. The negative slope can be interpreted as indicating the lack of correlation, whereas the positive slope indicates that the correlation between the independent variables is positive.
Heteroscedastics are also found in different kinds of distributions, such as binomial, exponential, Poisson and Gaussian distributions. Different kinds of distributions have different degrees of non-normality or the presence of heteroscedastics. For instance, the Poisson distribution has no normal curve; hence, it exhibits no homoscedastics.
Another type of distribution, known as clustering, has a significant degree of non-normality. This is the only type of distribution in which the significance of its mean differs from zero at some points. This type of distribution is most often used to make estimates of normal distributions. It exhibits a positive or negative mean slope, depending on the time interval over which the data is collected.
The Chi square distribution, on the other hand, has a significant degree of non-normality for the mean and its standard deviation is equal to twice the standard deviation of its distribution. Chi square distribution has a very low level of homoscedastics, and the mean and standard deviation are equal.
A normal distribution, which has no normal curve, can be described by a curve which contains a lot of points and a high degree of dispersion and a low degree of correlation. Therefore, in a normal distribution, the points are chosen so that the mean and the standard deviation are equal.
There are three types of distributions, which are described as non-normal, clustered, non-biclustered and chi-square. Non-normal distribution, which have no normal curve, can be defined by a curve, which has a high degree of non-normality for its mean and the standard deviation. Biclustered distributions, which have a high degree of non-normality have two or more high points on the curve, with a low degree of dispersion and low correlation. Chi square distribution, which has a large number of high points in the curve but a low degree of dispersion have no high and no low points in the curve.
A non-normal distribution is characterized by a curve, which contains high points and low points on the curve. It is therefore described by a curve that has high peaks and valleys, whereas a clustered distribution, which has high points on the curve and low points on the curve, can be described as a straight line, which has no peaks and no valleys. In this type of distribution, it is important to note that the degree of homoscedastics is almost exactly the same in all points in the curve.
The chi-square distribution is a distribution, which have a high degree of homoscedastics, and a low degree of non-normality, in its points. A chi-square distribution is therefore characterized by having a high and a low degree of homoscedasticity, at the tails of the curve.
There are other distribution models which have high levels of homoscedastics, but a low degree of non-normality, which include the Binomial distribution and the logistic distribution. In addition, there are still other distributions, which are characterized by high levels of homoscedastics, but no non-normality, for example the Fisher distribution, the Poisson distribution and the normal distribution.