|
|
 Login |
|
|
|
Volume 9 / Number 4, Summer 2006
Sampling Student’s T distribution – use of the inverse cumulative distribution function William T. Shaw
Department of Mathematics, King’s College, The Strand, London WC2R 2LS, UK With the current interest in copula methods, and fat-tailed or other non-normal distributions, it is appropriate to investigate technologies for managing marginal distributions of interest. We explore “Student’s” T distribution, survey its simulation, and present some new techniques for simulation. In particular, for a given real (not necessarily integer) value n of the number of degrees of freedom, we give a pair of power series approximations for the inverse, F−1 n , of the cumulative distribution function (CDF), Fn.We also give some simple and very fast exact and iterative techniques for defining this function when n is an even integer, based on the observation that for such cases the calculation of F−1 n amounts to the solution of a reduced-form polynomial equation of degree n − 1. We also explain the use of Cornish–Fisher expansions to define the inverse CDF as the composition of the inverse CDF for the normal case with a simple polynomial map. The methods presented are well adapted for use with copula and quasi-Monte-Carlo techniques.
|
|
|
|
| Subscribe to The Journal of Computational Finance and every quarter you will receive: |
• Innovative research papers written by leading academics in the field
• Detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments
• Online access to all research papers published in the history of the journal giving you access to a complete library of papers on computational finance
• Email Alerts notifying you when new issues are posted
To subscribe now click here. |
|
|
What to do if you do not know your username and password:
• If you are a The Journal of Computational Finance subscriber, click here and we will email you straight away with your username and password.
What to do if you are not a The Journal of Computational Finance subscriber:
• If you are not a The Journal of Computational Finance subscriber, click here to subscribe now or click here for a FREE sample.
Further information about The Journal of Computational Finance:
• Are you a new user? Click here for our guide.
• Are you having problems logging in to this website? Please click here for help. |
|
|
 |
 |
|
|
www.thejournalofcomputationalfinance.com |
|
|
|
|
|
|
|
|
|
|
|
|
|
The Risk Books and Journals group on 
is where editors, authors and readers can launch discussions about published and forthcoming books.
Click here to read these discussions and become part of the Risk Books and Journals group. |
|
|
