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Kurtosis: The extent to which the peak of the unimodal probability distribution or the frequency distribution departs from its shape of the normal distribution, by either being more pointed (like leptokurtic)or flatter ( like platykurtic). Commonly measured for a probability distribution as
where 4 is the fourth central moment of distribution, and 2 is its variance.
(consequent functions of sample moments are used for frequency distributions.)
For the normal distribution this index takes the value three and often index is redefined as the value above minus three so that the normal distribution would contain the value zero.
(Other distributions with the zero kurtosis are known as mesokurtic.) For the distribution which is leptokurtic the index is positive and for the platykurtic curves it is negative. It is shown in the figure
Cauchy distribution : The probability distribution, f (x), can be given as follows where α is the position of the parameter (median) and the beta β a scale parameter. Moments
difference between histogram and historigram
Evaluate the following statistical arguments. Begin by identifying the sample, population, and the property which is being investigated. Do these arguments sound acceptable? Would
Banach's match-box problem : The person carries two boxes of matches, one in his left and one in his right pocket. At first they comprise N number of matches each. When the person
Two-phase sampling is the sampling scheme including two distinct phases, in the first of which the information about the particular variables of interest is collected on all the m
Thomas Economic Forecasting, Inc. and Harmon Econometrics have the same mean error in forecasting the stock market over the last ten years. However, the standard deviation for Thom
The special cases of the probability distributions in which the random variable's distribution is concentrated at one point only. For instance, a discrete uniform distribution when
Normal approximation : Normal distributions which approximate other distributions; such as, a normal distribution with the mean np and variance np(1 - p) which acts as an approxima
McNemar's test is the test for comparing proportions in data involving the paired samples. The test statistic can be given by it is most useful when the data have a symmetri
Multiple imputation : The Monte Carlo technique in which missing values in the data set are replaced by m> 1 simulated versions, where m is usually small (say 3-10). Each of simula
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