 # What is cumulative distribution function? Can it be used in SPSS research?

What is cumulative distribution function? What are the properties of this function? Can it be used in SPSS research?

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Cumulative distribution function refers to the probability that the value of a random variable falls within a specified range. In this case if we add up all the probability density functions of a variable we should get one. This is because under any distribution the area under the curve is one or 100%.
SPSS researcher may be interested to what percentage falls under certain range of a distribution. In this case the best way to approach this situation is by using the cumulative distribution function.

Cumulative distribution function CDF is used by SPSS researchers to determine special ranges within a distribution so as to make appropriate decision making in a given situation.

From SPSS transform menu, compute. A dialogue box appears named compute variable. Name your target variable as CDF. In the same dialogue box there is a sub dialog box labeled functions, scroll down until you start to see the word CDF followed by the distribution you are dealing with. Select the CDF under consideration and click the arrow facing up so that it appears on the Numeric expression box. It will appear with question marks which you are supposed to fill with the appropriate parameters according to the distribution. Then click ok.

Looking at the data editor you will see additional variable CDF which guides you with 0 – 1 probabilities of the original variable. The researcher should note that the CDF values are adding up from each an every probability density function PDF up to one. If asked about certain range with respect to the variable under consideration(distribution function), the SPSS researcher should be able to look at the values of the variable and the values of the CDF representing the variable and deduct the lower limit from the upper limit of the range and multiply with a hundred to give an answer in percentage.