What is the coefficient of variation of the exponential distribution?

What is the coefficient of variation of the exponential distribution?

The standard deviation of an exponential distribution is equal to its mean, so its coefficient of variation is equal to 1.

What is acceptable coefficient of variation?

Definition of CV: The coefficient of variation (CV) is the standard deviation divided by the mean. CV% = SD/mean. CV<10 is very good, 10-20 is good, 20-30 is acceptable, and CV>30 is not acceptable.

How do you find the variance of an exponential distribution?

Let X be a continuous random variable with the exponential distribution with parameter β. Then the variance of X is: var(X)=β2.

What is a high coefficient of variation?

The coefficient of variation (CV) is the ratio of the standard deviation to the mean. The higher the coefficient of variation, the greater the level of dispersion around the mean. It is generally expressed as a percentage. The lower the value of the coefficient of variation, the more precise the estimate.

What is the exponential of a normal distribution?

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Equivalently, if Y has a normal distribution, then the exponential function of Y, X = exp(Y), has a log-normal distribution.

Can a covariance be used as a stepping stone to another statistical measure?

In reality, we’ll use the covariance as a stepping stone to yet another statistical measure known as the correlation coefficient. And, we’ll certainly spend some time learning what the correlation coefficient tells us. In regards to the second question, let’s answer that one now by way of the following theorem.

What is the covariance between X and Y?

Here, we’ll begin our attempt to quantify the dependence between two random variables X and Y by investigating what is called the covariance between the two random variables. We’ll jump right in with a formal definition of the covariance.

Which is the case of the standard exponential distribution?

The case where μ= 0 and β= 1 is called the standard exponential distribution. The equation for the standard exponential distribution is \\( f(x) = e^{-x} \\;\\;\\;\\;\\;\\;\\; \\mbox{for} \\; x \\ge 0 \\) The general form of probability functions can be expressed in terms of the standard distribution.

What is the Fisher information of an exponential distribution?

Fisher Information. The Fisher information, denoted , for an estimator of the rate parameter is given as: Plugging in the distribution and solving gives: This determines the amount of information each independent sample of an exponential distribution carries about the unknown rate parameter .