11.1 UNIFORM DISTRIBUTION CHARACTERISTICS

The uniform distribution is used to model the time of occurrence of events that are equally likely to occur at any time during an interval. The uniform pdf is given by [1, p. 96]

(11.1)

where ? is the location parameter and the value of ( ? - ?) represents the scale, or the range, of the pdf. Figure 11.1 shows the shape of the uniform pdf. Some specific characteristics of the uniform pdf are the following:

1. The uniform distribution takes on the value of in the interval ? ? T ? ?.

2. The mean, T, of the uniform pdf is

   (11.2)

3. The median, ?, of the uniform pdf is

   (11.3)

4. The mode, , of the uniform pdf is all values of T in the ? ? T ? ? range.

5. The standard deviation, ? _T, of the uniform pdf is

   (11.4)

6. The coefficient of skewness, ? ₃, of the uniform pdf is zero.

7. The coefficient of kurtosis, ? ₄, is

   (11.5)

8. The kth moment of the uniform pdf about the origin is

   (11.6)

9. The kth moment of the uniform pdf about the mean is

   
   

   or

   (11.7)

10. The relationships between the uniform and the beta pdf are:

    1. The uniform pdf is a special case of the beta pdf when the two parameters of the beta pdf are...