Tail Probability Approximations

Daniels, H. E.

doi:10.2307/1403269

Cited by 336 publications

(195 citation statements)

References 17 publications

Supporting

Mentioning

192

Contrasting

Order By: Relevance

“…Lugannani and Rice [42] approximated tail probabilities rather than densities. The following form of the Lugannani-Rice (LR) formula can be found in Daniels [23]:…”

Section: Saddlepoint Approximationmentioning

confidence: 99%

See 1 more Smart Citation

Saddlepoint approximations for affine jump-diffusion models

Glasserman¹,

Kim²

2009

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

“…Lugannani and Rice [42] approximated tail probabilities rather than densities. The following form of the Lugannani-Rice (LR) formula can be found in Daniels [23]:…”

Section: Saddlepoint Approximationmentioning

confidence: 99%

“…Lugannani and Rice [42] derive a saddlepoint approximation for the distribution function. See Daniels [23] and Jensen [37] for overviews of applications in statistics.…”

mentioning

confidence: 99%

Saddlepoint approximations for affine jump-diffusion models

Glasserman¹,

Kim²

2009

Journal of Economic Dynamics and Control

View full text Add to dashboard Cite

“…Of course, there are several loose ends in the derivation which should be formalized in order to be legitimate. Daniels (1954Daniels ( , 1987 presents all the details. Note that the fact that we are dealing with densities and random variables enters only in the derivation of the cumulant "'x(t) from the cumulants of the individual random variables.…”

Section: Saddlepoints For Sumsmentioning

confidence: 99%

Explaining the Saddlepoint Approximation

Casella¹,

Goutis²

1999

The American Statistician

View full text Add to dashboard Cite

George Casella* Cornell University Saddlepoint approximations are powerful tools for obtaining accurate expressions for densities and distribution functions. We give an elementary motivation and explanation of saddlepoint approximation techniques, stressing the connection with the familiar Taylor series expansions and the Laplace approximation of integrals. Saddlepoint methods are applied to the convolution of simple densities and, using the Fourier inversion formula, the saddlepoint approximation to the density of a random variable is derived. We then apply the method to densities of sample means of iid random variables, and also demonstrate the technique for approximating the density of a maximum likelihood estimator in exponential families.

show abstract

“…Two good review papers on the topic are Daniels (1987) and Reid (1988). Let T, be a real valued statistic and K,(t) be its cumulant generating function.…”

Section: Theory and Notationsmentioning

confidence: 99%

Small sample approximations for spacing statistics

Ghosh

Jammalamadaka

1998

Journal of Statistical Planning and Inference

View full text Add to dashboard Cite

Edgeworth expansions as well as saddle-point methods are used to approximate the distributions of some spacing statistics for small to moderate sample sizes. By comparing with the exact values when available, it is shown that a particular form of Edgeworth expansion produces extremely good results even for fairly small sample sizes. However, this expansion suffers from negative tail probabilities and an accurate approximation without this disadvantage, is shown to be the one based on saddle-point method. Finally, quantiles of some spacing statistics whose exact distributions are not known, are tabulated, making them available in a variety of testing contexts. (~)

show abstract

Tail Probability Approximations

Cited by 336 publications

References 17 publications

Saddlepoint approximations for affine jump-diffusion models

Saddlepoint approximations for affine jump-diffusion models

Explaining the Saddlepoint Approximation

Small sample approximations for spacing statistics

Contact Info

Product

Resources

About