How do you estimate the parameters of a normal distribution?
The common approach for estimating the parameters of a normal distribution is to use the mean and the sample standard deviation / variance. However, if there are some outliers, the median and the median deviation from the median should be much more robust, right?
What is maximum likelihood parameter estimation?
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
Can you use a normal distribution for skewed data?
No, your distribution cannot possibly be considered normal. If your tail on the left is longer, we refer to that distribution as “negatively skewed,” and in practical terms this means a higher level of occurrences took place at the high end of the distribution.
How do you find the maximum likelihood estimator?
Definition: Given data the maximum likelihood estimate (MLE) for the parameter p is the value of p that maximizes the likelihood P(data |p). That is, the MLE is the value of p for which the data is most likely. 100 P(55 heads|p) = ( 55 ) p55(1 − p)45. We’ll use the notation p for the MLE.
Is maximum likelihood estimator normally distributed?
“A method of estimating the parameters of a distribution by maximizing a likelihood function, so that under the assumed statistical model the observed data is most probable.” Let’s say we have some continuous data and we assume that it is normally distributed.
How is normal distribution different from skewed distribution?
In a normal distribution, the mean and the median are the same number while the mean and median in a skewed distribution become different numbers: A left-skewed, negative distribution will have the mean to the left of the median. A right-skewed distribution will have the mean to the right of the median.
How does skew affect standard deviation?
In a skewed distribution, the upper half and the lower half of the data have a different amount of spread, so no single number such as the standard deviation could describe the spread very well.