To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Johnson's SU-distribution

From Wikipedia, the free encyclopedia

Johnson's SU
Probability density function
JohnsonSU
Cumulative distribution function
Johnson SU
Parameters (real)
Support
PDF
CDF
Mean
Median
Variance
Skewness
Ex. kurtosis


The Johnson's SU-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949.[1][2] Johnson proposed it as a transformation of the normal distribution:[1]

where .

Generation of random variables

Let U be a random variable that is uniformly distributed on the unit interval [0, 1]. Johnson's SU random variables can be generated from U as follows:

where Φ is the cumulative distribution function of the normal distribution.

Johnson's SB-distribution

N. L. Johnson[1] firstly proposes the transformation :

where .

Johnson's SB random variables can be generated from U as follows:

The SB-distribution is convenient to Platykurtic distributions (Kurtosis). To simulate SU, sample of code for its density and cumulative distribution function is available here

Applications

Johnson's -distribution has been used successfully to model asset returns for portfolio management.[3] This comes as a superior alternative to using the Normal distribution to model asset returns. An R package, JSUparameters, was developed in 2021 to aid in the estimation of the parameters of the best-fitting Johnson's -distribution for a given dataset. Johnson distributions are also sometimes used in option pricing, so as to accommodate an observed volatility smile; see Johnson binomial tree.

An alternative to the Johnson system of distributions is the quantile-parameterized distributions (QPDs). QPDs can provide greater shape flexibility than the Johnson system. Instead of fitting moments, QPDs are typically fit to empirical CDF data with linear least squares.

Johnson's -distribution is also used in the modelling of the invariant mass of some heavy mesons in the field of B-physics.[4]

References

  1. ^ a b c Johnson, N. L. (1949). "Systems of Frequency Curves Generated by Methods of Translation". Biometrika. 36 (1/2): 149–176. doi:10.2307/2332539. JSTOR 2332539.
  2. ^ Johnson, N. L. (1949). "Bivariate Distributions Based on Simple Translation Systems". Biometrika. 36 (3/4): 297–304. doi:10.1093/biomet/36.3-4.297. JSTOR 2332669.
  3. ^ Tsai, Cindy Sin-Yi (2011). "The Real World is Not Normal" (PDF). Morningstar Alternative Investments Observer.
  4. ^ As an example, see: LHCb Collaboration (2022). "Precise determination of the  oscillation frequency". Nature Physics. 18: 1–5. arXiv:2104.04421. doi:10.1038/s41567-021-01394-x.

Further reading

  • Hill, I. D.; Hill, R.; Holder, R. L. (1976). "Algorithm AS 99: Fitting Johnson Curves by Moments". Journal of the Royal Statistical Society. Series C (Applied Statistics). 25 (2).
  • Jones, M. C.; Pewsey, A. (2009). "Sinh-arcsinh distributions" (PDF). Biometrika. 96 (4): 761. doi:10.1093/biomet/asp053.( Preprint)
  • Tuenter, Hans J. H. (November 2001). "An algorithm to determine the parameters of SU-curves in the Johnson system of probability distributions by moment matching". The Journal of Statistical Computation and Simulation. 70 (4): 325–347. doi:10.1080/00949650108812126. MR 1872992. Zbl 1098.62523.
This page was last edited on 5 January 2024, at 18:58
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.