# Hansmann’s Distributions

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Hansmann’s distributions , obtained from a generalized Pearson differential equation , are symmetric about zero.

They are derived from Pearson’s equation Which becomes The probability density functions [which Johnson et al  notes contain a correction by Pawula & Rice ) are:   Where

• K= ½ {c2(b2 – a2)}-1
• K, K1, K2 are normalizing constants.

K1 and K2 must satisfy the conditions

• ∫P(x)dx = 1
• ∫x2p(x)= σ2x.

## References

 Hansmann, G. H. (1934). On certain non-normal symmetric frequency distributions, Biometrika, 26, 129-135

 Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.

 Johnson, Kotz, and Balakrishnan, (1994), Continuous Univariate Distributions, Volumes I and II, 2nd. Ed., John Wiley and Sons.

 Pawula, R. F., and Rice, S. 0. (1989). A note on Hansmann’s 1934 family of distributions, IEEE Transactions on Information Theory, 35, 910-91 1.

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Stephanie Glen. "Hansmann’s Distributions" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/hansmanns-distributions/
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