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Can the value of a cumulative distribution function be greater than one?
A pf gives a probability, so it cannot be greater than one. A pdf f(x), however, may give a value greater than one for some values of x, since it is not the value of f(x) but the area under the curve that represents probability.
What is approximating distribution?
Key Terms. normal approximation: The process of using the normal curve to estimate the shape of the distribution of a data set. central limit theorem: The theorem that states: If the sum of independent identically distributed random variables has a finite variance, then it will be (approximately) normally distributed.
How are the parameters of a distribution calculated?
The following techniques of distribution fitting exist: Parametric methods, by which the parameters of the distribution are calculated from the data series. The parametric methods are: (the variance) can be estimated from the standard deviation of the data. The mean is found as .
Can a probability distribution be used if x is less than zero?
Some probability distributions, like the exponential, do not support data values ( X) equal to or less than zero. Yet, when negative data are present, such distributions can still be used replacing X by Y = X – Xm, where Xm is the minimum value of X.
When to use normal distribution or logistic distribution?
When the data are symmetrically distributed around the mean while the frequency of occurrence of data farther away from the mean diminishes, one may for example select the normal distribution, the logistic distribution, or the Student’s t-distribution.
Why does the true probability distribution deviate from the fitted distribution?
The true probability distribution of events may deviate from the fitted distribution, as the observed data series may not be totally representative of the real probability of occurrence of the phenomenon due to random error