Functions > Statistics > Probability Distributions > Example: Generating Random Numbers
Example: Generating Random Numbers
Create vectors of random numbers that are respectively uniformly distributed, normally distributed, or exponentially distributed over an interval.
Uniformly Distributed
1. Call function runif to generate n_set random numbers that are uniformly distributed between low and high.
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2. Use function hist to generate a histogram of the uniform set with n_bins bins, then calculate the mean of the set.
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3. Plot the histogram and show the expected mean for the data set:
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To get a new set of random numbers, on the Calculation tab, in the Controls group, click Calculate. A new seed value is used to generate random numbers each time you recalculate.
Normally Distributed
1. Call function rnorm to generate n_set random numbers having the normal distribution with mean μ and standard deviation σ.
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2. Use functions floor, ceil, min and max to calculate the minimum and the maximum range of the data set, then calculate the width of each bin:
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3. Set the horizontal scale for the plot:
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4. Call function dnorm to calculate the normal distribution F expected for the data set, then plot a histogram of the normal set with n_bins bins.
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Exponentially Distributed
1. Call function rexp to generate a set of random numbers that are exponentially distributed with rate r.
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2. Call function dexp to calculate the exponential distribution F expected for the data set, then plot a histogram of the exponential set with n_bins bins.
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3. Call functions pexp and qexp to calculate and plot the cumulative probability distribution for value x and the inverse cumulative probability distribution for value p, respectively.
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The first argument of function qexp is probability and must be less than 1, hence the division of int by 100.
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