Let's calculate the cumulative probabilities for the distribution above: from scipy.stats import uniform We can observe that all values have an equal probability of happening. Let's now calcuate the probabilities for a given uniform distribution: from scipy.stats import uniform All the values are uniformly distributed in this distribution. We can observe that the bars have a similar height. # generate uniformly distributed random numbers # if you want to maintain reproducibility Let's first see how can we generate a random uniform distribution: from scipy.stats import uniform # generates an array of random numbers of the given uniform distribution Use the CDF to determine the probability that a random observation that is taken from the population will be less than or equal to a certain value. # returns cumulative value corresponding to probability value The cumulative distribution function (CDF) calculates the cumulative probability for a given x-value. # measures cumulative distribution function (cdf) of the distribution
We will utilize the methods in this tutorial: # measures the probability density function (pdf) of the distribution The numpy and SciPy libraries both provide all methods required to generate and calculate a uniform distribution. Recall that the CDF shows the probability that the random variabel X will take a value less than or equal to x: The cumulative distribution function (CDF) of the uniform distribution is defined as follows. The mean of the uniform distribution is defined as (a+b)/2, and the variance as (b-a)**2/12. Where a and b are the lower and upper boundaries which make up the minimum and maximum value of the distribution. The probability density function (CDF) of uniform distribution is defined as: In a discrete uniform distribution, outcomes are discrete numbers such as non-negative integers, and in a continuous distribution, outcomes are continuous and infinite. The uniform distribution can be discrete or continuous. For example, rolling a fair die will produce a uniform distribution, because each side from 1 to 6 has equal probability of facing up. That means all outcomes have the equal chance of happening in the uniform distribution. From definition I have that the cdf is given by F ( x) x f ( t) d t So I will split it up to 3 intervals: If x < a we have that f ( x) 0 so F ( x) 0 here.
#Cdf of uniform distribution pdf#
The uniform distribution is concerned with events that are equally likely to occur. 5 I have that the pdf for a uniform distribution is given by f ( x) 1 b a if a x b and 0 otherwise.
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