Truncated Normal Spread Ratio

  • Nick T. Thomopoulos


A new statistic, called the spread ratio, is introduced that allows the analyst to identify which distribution best fits sample data, where the choice of distributions are the normal, left-truncated normal (LTN), and right-truncated normal (RTN). When the choice is the LTN or RTN, the location parameter, k, is also identified. The spread ratio for each distribution is computed using percent-points, t0.01, t0.99, and the mean of the distribution, and is a positive number. Using sample data, an estimate of the spread ratio is easily measured, and when the ratio is near one, the normal distribution fits the data best; when below one, the LTN is chosen; and when above one, the RTN is selected. For LTN, the low limit of the population data, γ, is estimated with use of the sample data and the tables provided on LTN. In the same way, if the RTN is chosen as the distribution, the high limit, δ, of the population data is easily estimated using sample data and the tables on RTN. Further, in either event, LTN or RTN, the analysis allows the researcher to estimate a value xα, where P(x ≤ xα) = α. Also when LTN or RTN, the analysis shows how to estimate the value of α for a given x` where P(x ≤ x`) = α.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Nick T. Thomopoulos
    • 1
  1. 1.Stuart School of BusinessIllinois Institute of TechnologyChicagoUSA

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