#### Generate random variable from uniform distribution

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Documentation Help Center. This example shows how to generate random numbers using the uniform distribution inversion method. This is useful for distributions when it is possible to compute the inverse cumulative distribution function, but there is no support for sampling from the distribution directly. Use rand to generate random numbers from the uniform distribution on the interval 0,1.

The inversion method relies on the principle that continuous cumulative distribution functions cdfs range uniformly over the open interval 0,1. Plot the results. The histogram shows that the random numbers generated using the Weibull inverse cdf function wblinv have a Weibull distribution. The same values in u can generate random numbers from any distribution, for example the standard normal, by following the same procedure using the inverse cdf of the desired distribution. The histogram shows that, by using the standard normal inverse cdf norminvthe random numbers generated from u now have a standard normal distribution. A modified version of this example exists on your system. Do you want to open this version instead? Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance.

Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation. Search Support Support MathWorks. Search MathWorks. Open Mobile Search. Off-Canvas Navigation Menu Toggle. Generate random numbers from the standard uniform distribution. Step 2. Generate random numbers from the Weibull distribution. Step 3.

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Generate random numbers from the standard normal distribution.In probability theory and statisticsthe continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The interval can be either be closed eg. It is the maximum entropy probability distribution for a random variable X under no constraint other than that it is contained in the distribution's support.

The probability density function of the continuous uniform distribution is:. The latter is appropriate in the context of estimation by the method of maximum likelihood. Also, it is consistent with the sign function which has no such ambiguity.

As the distance between a and b increases, the density at any particular value within the distribution boundaries decreases.

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In graphical representation of uniform distribution function [f x vs x], the area under the curve within the specified bounds displays the probability shaded area is depicted as a rectangle. The cumulative distribution function is:. The moment-generating function is: . One interesting property of the standard uniform distribution is that if u 1 has a standard uniform distribution, then so does 1- u 1.

This property can be used for generating antithetic variatesamong other things. In other words, this property is known as the inversion method where the continuous standard uniform distribution can be used to generate random numbers for any other continuous distribution. As long as the same conventions are followed at the transition points, the probability density function may also be expressed in terms of the Heaviside step function :. There is no ambiguity at the transition point of the sign function.

Using the half-maximum convention at the transition points, the uniform distribution may be expressed in terms of the sign function as:. The mean first moment of the distribution is:.

The variance second central moment is:. Let X k be the k th order statistic from this sample. The expected value is.

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The probability that a uniformly distributed random variable falls within any interval of fixed length is independent of the location of the interval itself but it is dependent on the interval sizeso long as the interval is contained in the distribution's support. This distribution can be generalized to more complicated sets than intervals.I describe how to generate random numbers and discuss some features added in Stata In particular, Stata 14 includes a new default random-number generator RNG called the Mersenne Twister Matsumoto and Nishimuraa new function that generates random integers, the ability to generate random numbers from an interval, and several new functions that generate random variates from nonuniform distributions.

In the example below, we use runiform to create a simulated dataset with 10, observations on a 0,1 -uniform variable. Prior to using runiformwe set the seed so that the results are reproducible.

### Generating random variables

The mean of a 0,1 -uniform is. The estimates from the simulated data reported in the output below are close to the true values. To draw uniform variates over a, b instead of over 0, 1we specify runiform a, b.

In the example below, we draw uniform variates over 1, 2 and then estimate the mean and the standard deviation, which we could compare with their theoretical values of 1. We use set seed to obtain the same random numbers, which makes the subsequent results reproducible.

RNGs come from a recursive formula. Setting the seed specifies a starting place for the recursion, which causes the random numbers to be the same, as in the example below.

## Uniform distribution

Larger periods are better because we get more random numbers before the sequence wraps. Large periods are important when performing complicated simulation studies. The state of an RNG corresponds to a spot in the sequence. The mapping is not one to one because there are more states than seeds. If you want to pick up where you left off in the sequence, you need to restore the state, as in the example below.

After dropping the data and setting the number of observations to 3, we use generate to put random variates in xstore the state of the RNG in the local macro stateand then put random numbers in y. Next, we use set rngstate to restore the state to what it was before we generated yand then we generate z. The random numbers in z are the same as those in y because restoring the state caused Stata to start at the same place in the sequence as before we generated y.

How to generate random numbers from continuous uniform distribution - model sampling - simulation

See Programming an estimation command in Stata: Where to store your stuff for an introduction to local macros. So far, we have talked about generating uniformly distributed random numbers. Stata also provides functions that generate random numbers from other distributions.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

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It only takes a minute to sign up. I'm not looking for an exact answer as much as an explanation to help with these problems in the future. Use the following idea. And so on. It doesn't really matter what we do. If a description in terms of the cdf is required, please indicate.

Email Required, but never shown. Featured on Meta. Responding to the Lavender Letter and commitments moving forward. Related 0. Hot Network Questions. Question feed. Mathematics Stack Exchange works best with JavaScript enabled.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. How can I convert a uniform distribution as most random number generators produce, e.

What if I want a mean and standard deviation of my choosing? The Ziggurat algorithm is pretty efficient for this, although the Box-Muller transform is easier to implement from scratch and not crazy slow. Changing the distribution of any function to another involves using the inverse of the function you want.

Now use the random probability function which have uniform distribution and cast the result value through the function Inv d x. You should get random values cast with distribution according to the function you chose. This is the generic math approach - by using it you can now choose any probability or distribution function you have as long as it have inverse or good inverse approximation.

Hope this helped and thanks for the small remark about using the distribution and not the probability itself. Use the central limit theorem wikipedia entry mathworld entry to your advantage. If you want something more than half decent go for tylers solution as noted in the wikipedia entry on normal distributions. It seems incredible that I could add something to this after eight years, but for the case of Java I would like to point readers to the Random.

The manual entry is here. This will product the random numbers which should be normally distributed with the zero mean and unite variance. Q How can I convert a uniform distribution as most random number generators produce, e.

For software implementation I know couple random generator names which give you a pseudo uniform random sequence in [0,1] Mersenne Twister, Linear Congruate Generator. Let's call it U x. It is exist mathematical area which called probibility theory.

## Generate Random Numbers Using Uniform Distribution Inversion

First thing: If you want to model r. In pr. Step 2 can be appliable to generate r. This is a Matlab implementation using the polar form of the Box-Muller transformation:.A continuous random variable has a uniform distribution if all the values belonging to its support have the same probability density.

Definition Let be a continuous random variable. Let its support be a closed interval of real numbers: We say that has a uniform distribution on the interval if and only if its probability density function is.

A random variable having a uniform distribution is also called a uniform random variable. Sometimes, we also say that it has a rectangular distribution or that it is a rectangular random variable. To better understand the uniform distribution, you can have a look at its density plots.

The expected value of a uniform random variable is. It can be derived as follows:. The variance of a uniform random variable is. We can use the variance formula as follows:. The moment generating function of a uniform random variable is defined for any :.

Using the definition of moment generating function, we get Note that the above derivation is valid only when. However, when : Furthermore, it is easy to verify that Whenthe integral above is well-defined and finite for any. Thus, the moment generating function of a uniform random variable exists for any. The characteristic function of a uniform random variable is.

Using the definition of characteristic function, we obtain Note that the above derivation is valid only when. However, when : Furthermore, it is easy to verify that. The distribution function of a uniform random variable is. Ifthen because can not take on values smaller than. Ifthen Ifthen because can not take on values greater than. This section shows the plots of the densities of some uniform random variables, in order to demonstrate how the uniform density changes by changing its parameters.

The two random variables have different supports, but their two supports have the same length. Therefore, since the uniform density is constant and inversely proportional to the length of the support, the two random variables have the same constant density over their respective supports. The two random variables have different supports, and the length of is twice the length of. Therefore, since the uniform density is constant and inversely proportional to the length of the support, the second random variable has a constant density which is half the constant density of the first one.

Let be a uniform random variable with support Compute the following probability:. We can compute this probability by using the probability density function or the distribution function of.

Using the probability density function, we obtain Using the distribution function, we obtain. Suppose the random variable has a uniform distribution on the interval. Compute the following probability:. This probability can be easily computed by using the distribution function of :. Compute the third moment ofthat is. We can compute the third moment of by using the transformation theorem :.

### Using the uniform random variable to generate other random variables

Taboga, Marco Kindle Direct Publishing.Documentation Help Center. For example, rand 3,4 returns a 3-by-4 matrix. For example, rand [3 4] returns a 3-by-4 matrix. The typename input can be either 'single' or 'double'. You can use any of the input arguments in the previous syntaxes. You can specify either typename or 'like'but not both. To create a stream, use RandStream. Specify s followed by any of the argument combinations in previous syntaxes, except for the ones that involve 'like'.

This syntax does not support the 'like' input. The 'seed''state'and 'twister' inputs to the rand function are not recommended. Use the rng function instead. For more information, see Replace Discouraged Syntaxes of rand and randn. Generate a 5-by-5 matrix of uniformly distributed random numbers between 0 and 1. Generate a by-1 column vector of uniformly distributed numbers in the interval -5,5.

Use the randi function instead of rand to generate 5 random integers from the uniform distribution between 10 and Generate a single random complex number with real and imaginary parts in the interval 0,1.

Save the current state of the random number generator and create a 1-by-5 vector of random numbers. Restore the state of the random number generator to sand then create a new 1-by-5 vector of random numbers.

The values are the same as before. Always use the rng function rather than the rand or randn functions to specify the settings of the random number generator.

Create an array of random numbers that is the same size and data type as p. For the distributed data type, the 'like' syntax clones the underlying data type in addition to the primary data type. Create an array of random numbers that is the same size, primary data type, and underlying data type as p. If n is 0then X is an empty matrix.

If n is negative, then it is treated as 0. Data Types: single double int8 int16 int32 int64 uint8 uint16 uint32 uint If the size of any dimension is 0then X is an empty array. Beyond the second dimension, rand ignores trailing dimensions with a size of 1.

For example, rand 3,1,1,1 produces a 3-by-1 vector of random numbers. Size of each dimension, specified as a row vector of integer values.