Probability Distribution

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A probability distribution is a mathematical function which describes the probabilities and possible outcomes that an unpredictable, complex, and continuous variable could take in a given discrete range. This range would generally be bounded between the maximum and minimum probable values, though the exact location of this probability distribution often depends on many factors. Probability distributions are most commonly used in forecasting, especially in inventory or production estimating, and are an important tool for statistical analysis. In fact, most statistical studies of manufacturing, sales, distribution, consumption, planning, and economic activity actually rely on a probabilistic distribution. This is because the distribution of events, or outputs, can provide the aggregated output of an unpredictable process, thus allowing researchers to approximate the range of possible future outputs with an accurate statistical estimate of the distribution of input parameters.

One of the most widely used probabilistic distributions is the binomial probability distribution, which depicts the probability that the random variables will occur in a finite, discrete range. The underlying assumption of the binomial distribution is that the distribution of events occurs in a closed process in which the random variables are assumed to have independent probability. This type of distribution is used extensively in scientific studies of probability, including frequency functions and geometric distributions. Probability distributions may also be discrete, or closed, in which case they are referred to as Black-Lagrange or log-normal distributions. The discrete log-normal distribution (often denoted as logit) depicts the probability distribution of the log-likelihood function, which is a mathematical equation that estimates the probability that a normal log curve will lie somewhere close to a single exponential curve.

Another common probability distribution is the logistic distribution, which depicts the probability that the random variables will occur in a continuous range. The log-normal distribution closely resembles the binomial distribution, in that it depicts the probability that the random variables will occur in discrete ranges as well. Some important points to remember about the probability distributions mentioned above are that they are usually used to illustrate the probability that the outcomes of an experiment will occur as expected, and they can be presented in a number of different ways. While they are fairly simple in appearance, they are more complex when presented in images or graphs. They are also very useful for visualizing the results obtained from experiments on real data sets.

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