Retrospection with a New Purpose: Applying the Laplace Distribution to Chemical Engineering Problems


(*) Corresponding author


Authors' affiliations


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


Originating from the late eighteenth century and well known in contemporary probability theory, the Laplace distribution seems to have penetrated only into certain segments of scientific and engineering endeavors. This paper indicates its potential of representing adequately the random character of some phenomena of chemical engineering interest, and its capability of offering an admissible option vis-à-vis the traditional normal (Gaussian) distribution. A concise description of underlying theory is followed by quantitative illustrations taken from the textbook literature, where interpretation of material in terms of the normal distribution is prescribed. Nonetheless, choice of the level of significance in goodness-of-fit tests determines whether the Laplace distribution is, indeed, a viable alternative to the normal
Copyright © 2014 Praise Worthy Prize - All rights reserved.

Keywords


Goodness-of-Fit Tests; Maximum Likelihood Estimators; Chemical Applications

Full Text:

PDF


References


M. Evans, N. Hastings, B. Peacock, Statistical Distributions (Wiley and Sons, 2000, pp.117-120) Chapter 23.

S. Katz, T.J. Kuzobowski, K. Polgόrski, The Laplace Distribution and Generalizations-A Revisit with Applications to Communications, Engineering and Finance (Birkhäuser, 2001).

E. Parzen, Modern Probability Theory and Its Applications (Wiley and Sons, 1960, p.354) Exercise 1.14

E. Parzen, Modern Probability Theory and Its Applications (Wiley and Sons, 1960, pp.398-399) Exercise 2D.

E. Parzen,Modern Probability Theory and Its Applications (Wiley and Sons, 1960, pp.396-399.)

A. Papoulis, Probability and Statistics (Prentice Hall, 1990, p.166). Problem 5.18.

Fan Wu, Applications of the Normal Laplace and the Generalized Normal Laplace Distributions, M.Sc. dissertation, Dept. of Math.,Univ. of Victoria, BC,2008.

D. Kundu, Discriminating Between the Normal and Laplace Distribution, Wikipedia, home.iitk.ac.in/ ~kundu/paper98.pdf

E. Damsleth, A. H. El-Shaarawi, ARMA Models with Double-Exponentially Distributed Noise, J. Royal Statist . Soc. Ser.B51 (1989)61-69.

R.M. Morton, The Double Exponential Distribution: Using Calculus to Find a MLE, Amer. Statist. 38(1943) 135-136.

The Laplace Distribution, Wikipedia [12] G. Keller, B. Warrack, Statistics for Management and Economics (Duxbury, 2000, pp.544-551).

R.L. Scheaffer, J.T. McClave, Probability and Statistics for Engineers (Duxbury, 1986, pp. 335-337), Section 7.5.

M.A. Stephens, EDF Statistics for Goodness of Fit and Some Comparisons, J.Amer.Stat.Assoc. 69(1974)730-737.

R.L. Scheaffer, J.T. McClave, Probability and Statistics for Engineers(Duxbury,1986, p.329) Table 7.5.

G.M. Jenkins, D.G. Watts, Spectral Analysis (Holden Day, 1968).

H. Jeffreys, The Theory of Probability (Clarendon Press, 1961).

P. M. Reilly, Statistical Methods in Model Discrimination, Can.J.Chem.Eng. 48(1970)168-173.

D.Kundu, Discriminating Between the Normal and Laplace Distribution, Wikipedia. home.iitk.ac.in/~kundu/paper98.pdf p.5, Eq.(4).

H. White, Maximum Likelihood Estimation of Mis- specified Models, Econometrica, 50(1982)1-25.

H. White, Regularity Conditions for Cox’s Test of Non- Nested Hypotheses, J. Econometr., 19(1982)301-318.

S.B. Vardeman, Statistics for Engineering Problem Solving (PWS Publishing, 1994, p.98)Problem 3-23.

S.B. Vardeman, Statistics for Engineering Problem Solving (PWS Publishing, 1994, p.96)Exercise 3.15.

R. Porkess, Collins Dictionary of Statistics (HarperCollins, 2005, p.133).

R. Porkess, Collins Dictionary of Statistics (HarperCollins, 2005, p.308) Table 15.

J. F. Lawless, Statistical Models and Methods for Lifetime Data (J.Wiley and Sons,1982). [27] S. Kotz, T.J. Kozubowski, K.Polgόrski, The Laplace Distribution and Generalizations-A Revisit with Applications To Communications, Engineering and Finance (Birkhäuser, 2001, p.222).Exercise 4.5.1.

S. Kotz, T.Z. Kozubowski, K. Polgόrski, The Laplace Distribution and Generalizations-A Revisit with Applications To Communications, Engineering and Finance (Birkhäuser, 2001, p.3).

D.V. Lindsey, W.F. Scott, New Cambridge Statistical Tables(CUP,1984,p.35)Table 5.


Refbacks

  • There are currently no refbacks.


Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize