The statement that a parameter is a " location parameter " is that the sampling distribution, or likelihood of an observation " X " depends on a parameter \ mu only through the difference
32.
For example, when estimating a location parameter for a symmetric distribution, a trimmed estimator will be unbiased ( assuming the original estimator was unbiased ), as it removes the same amount above and below.
33.
Such a parameter must affect the " shape " of a distribution rather than simply shifting it ( as a location parameter does ) or stretching / shrinking it ( as a scale parameter does ).
34.
But, unlike in the location parameter case, the Jacobian of this transformation in the sample space and the parameter space is " a ", not 1 . so the sampling probability changes to:
35.
One situation in which it can be advantageous to use a truncated mean is when estimating the location parameter of a Cauchy distribution, a bell shaped probability distribution with ( much ) fatter tails than a normal distribution.
36.
:where the value of the summand is taken to be zero when \ theta + 2 \ pi n-\ mu \ le 0, c is the scale factor and \ mu is the location parameter.
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In this case, all the year, month, day and location parameters, except the last, must be supplied, but as before, month and day may be left empty or blank if not known.
38.
When the median is used as a location parameter in descriptive statistics, there are several choices for a measure of variability : the range, the interquartile range, the mean absolute deviation, and the median absolute deviation.
39.
Specifically, a shape parameter is any parameter of a probability distribution that is neither a location parameter nor a scale parameter ( nor a function of either or both of these only, such as a rate parameter ).
40.
Where p ( x; \ alpha, 1, c, 0 ) is the pdf of a one-sided continuous-stable distribution with symmetry param�tre \ beta = 1 and location parameter \ mu = 0.
