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What is variance distribution?
a small standard deviation (or variance) means that the distribution of the random variable is narrowly concentrated around the mean. a large standard deviation (or variance) means that the distribution is spread out, with some chance of observing values at some distance from the mean.
What is the formula for variance of binomial distribution?
The variance of the binomial distribution is s2=Np(1−p) s 2 = Np ( 1 − p ) , where s2 is the variance of the binomial distribution.
When does a random variable have a compound distribution?
The random variable is said to have a compound distribution if is of the following form where (1) the number of terms is uncertain, (2) the random variables are independent and identically distributed (with common distribution ) and (3) each is independent of .
When do frequency and severity are independent how is compound variance calculated?
When frequency and severity are independent, the following shortcut is valid and is called a compound variance: Variance under the individual risk model is additive: Example 2: Continuing from Example 1, calculate the mean and variance of the aggregate loss. Assume frequency and severity are independent.
Which is a special case of compound distribution?
Convolution of probability distributions (to derive the probability distribution of sums of random variables) may also be seen as a special case of compounding; here the sum’s distribution essentially results from considering one summand as a random location parameter for the other summand.
When do you use a compound variance shortcut?
When frequency and severity are independent, the following shortcut is valid and is called a compound variance: Variance under the individual risk model is additive: Example 2: Continuing from Example 1, calculate the mean and variance of the aggregate loss.