# Truncated Normal Distribution

Truncated Normal Statistical Distribution

General Characteristics

• Truncated Normal Distribution is derived from a normally distributed random variable, by bounding the random variable from either below, above or both.
• Truncations can be either; one-sided of lower tail truncation, one-sided of upper tail truncation or two-sided truncation.

Specific Characteristics

Key Measures:

Mean, Standard Deviation (SD), Lower Limit, Upper Limit

Range of values:

lower limit <= x < ∞ (if the lower limit is specified),
-∞ < x <= upper limit (if the upper limit is specified) &
lower limit <= x <= upper limit (if both limits are specified)

Mean:

Mean = mean

Standard Deviation, SD:

SD = sd

Application

Truncated Normal distributions can be used to find errors in dimensions of components, like its ‘parent’ distribution – Normal distribution, but avoids the Normal distribution problem of extreme values, especially negative values.

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