You may need to model non-deterministic processes, e.g. product demand changing, product processing time, or speed of a certain vehicle. Stochastic processes can be defined using probability distributions.
ALX comes with a set of probability distributions.
The Uniform distribution is a continuous distribution bounded on both sides, i.e. the sample lays in the interval [min,max). The probability density does not depend on the value of x. It is a special case of the Beta distribution. It is frequently called rectangular distribution (see Johnson et al).
The Uniform distribution is used to represent a random variable with constant likelihood of being in any small interval between min and max. Note that the probability of max value is 0; the max point never occurs.
Name Type Description min double the minimum x value max double the maximum x value
The Triangular distribution is a continuous distribution
The Triangular distribution is often used when no or little data is available; it is rarely an accurate representation of a data set. However, it is employed as the functional form of regions for fuzzy logic due to its ease of use.
The Triangular distribution can take on very skewed forms including negative skewness. For the exceptional cases where the mode is either the min or max, the Triangular distribution becomes a right triangle.
Name Type Description min double the minimum x value max double the maximum x value mode double the most likely x value
The Exponential distribution is a continuous distribution bounded on the lower side. It’s shape is always the same, starting at a finite value at the minimum and continuously decreasing at larger x. The Exponential distribution decreases rapidly for increasing x.
The Exponential distribution is frequently used to represent times of a specific operation.
Name Type Description lambda double the shape parameter min double the minimum x value
The Normal distribution is an unbounded continuous distribution. It is sometimes called a Gaussian distribution or the bell curve. Because of its property of representing an increasing sum of small, independent errors, the Normal distribution finds many uses in statistics. It is wrongly used in many situations. Possibly, the most important test in the fitting of analytical distributions is the elimination of the Normal distribution as a possible candidate.
The Normal distribution is frequently used to represent symmetrical data, but suffers from being unbounded in both directions. If the data is known to have a lower bound, it may be better represented by suitable parameterization of the Lognormal distribution.
Name Type Description sigma double the shape parameter = standard deviation mean double the shift parameter = mean value
The Lognormal distribution is a continuous distribution bounded on the lower side. It is always 0 at minimum x, rising to a peak that depends on both mu and sigma, then decreasing monotonically for increasing x.
Name Type Description mu double the mean of the included Normal sigma double the standard deviation of the included Normal min double the minimum x value