The Erlang distribution can be used to model the time to complete n operations in series, where each operation requires an exponential period of time to complete.
The Erlang distribution is utilized to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has been expanded to consider waiting times in queueing systems in general. The distribution is now used in the fields of stochastic processes and of biomathematics.
The intervals between call arrivals is then an Exponential distribution, and the sum of k such distributions is an Erlang distribution (i.e. the time before the kth call arrives), so the Poisson, Exponential, Erlang and Gamma distributions are very closely related to one another.
For the Erlang Distribution App three data parameters for the Real Rate of Change ( λ ), Scale ( μ ) and Shape ( k ) are input via sliders to compute PDF and CDF values and the Erlang mean and variance. The PDF and CDF values are displayed both in data table and graph forms.
The PDF and CDF graphs are touch interactive graphs for computed (x/Pr(x) paired values. The graphs have a touch feature whereby upon the touch a slidable vertical line appears. Upon movement of the line a paired (x,Pr(x) values appear relative to the line position on the graph curve.
The horizontal x-axis displays computed (x) values. The vertical y-axis plots a range of Pr(x) values.
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- Donald Schaefer
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