where (provided and exist and are real).
By multiplying both sides of the recursive formula by , you get
which shows that the left side is obviously a linear function of . When using a sample of data, an approximation of the 's need to be done. If represents the number of observations having the value , then is an unbiased estimator of the true .
Therefore, if a linear trend is seen, then it can be assumed that the data is taken from an (a,b,0) distribution. Moreover, the slope of the function would be the parameter , while the ordinate at the origin would be .
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