11. Right Truncated Normal

In 2001, Arvid Johnson and Nick Thomopoulos generated tables on the right-truncated normal distribution. The right-truncated normal (RTN) takes on a variety of shapes from normal to exponential-like. The distribution has one parameter k where the range includes all values of the standard normal that is less than a value of z = k. In this way, the distribution has the shape of the standard normal on the left and is truncated on the right. The variable is denoted as t and t is zero or negative throughout. With k specified, the following statistics are computed: the mean, standard deviation, coefficient-of-variation, and 0.01% and 0.99% points of t. The spread ratio of the RTN is also computed for each parameter value of k. A table is generated that lists all these statistics for values of k ranging from −3.0 to +3.0. When sample data is available, the analyst computes the following statistics: sample average, standard deviation, min and max. From these, the estimate of the spread ratio is computed, and this estimate is compared to the table values to locate the parameter k that has the closest value of θ. With k estimated for the sample data, the analyst identifies the RTN distribution that best fits the data. From here, the high-limit δ can be estimated, and also any α-percent-point on x that may be needed. The spread-ratio test sometimes indicates the sample data is best fit by the normal distribution, and on other situations by the RTN.