Multivariate normal-Laplace distribution and processes


  • Kanichukattu K. Jose St. Thomas College, Mahatma Gandhi University, Kottayam - Kerala
  • Manu Mariam Thomas St. Thomas College, Mahatma Gandhi University, Kottayam - Kerala



multivariate normal-Laplace distribution, autoregressive processes, multivariate geometric normal-Laplace distribution, multivariate geometric generalized normal-Laplace distribution


The normal-Laplace distribution is considered and its properties are discussed. A multivariate normal-Laplace distribution is introduced and its properties are studied. First order autoregressive processes with these stationary marginal distributions are developed and studied. A generalized multivariate normal-Laplace distribution is introduced. Multivariate geometric normal-Laplace distribution and multivariate geometric generalized normal-Laplace distributions are introduced and their properties are studied. Estimation of parameters and some applications are also discussed.


P. BLAESID (1981). The two-dimensional hyperbolic distribution and related distributions, with an application to Johannsen's bean data. Biometrika, 68, pp. 251-263.

E. DAMSLETH, A.H. EL-SHAARAWI (1989). ARMA models with double-exponentially distributed noise. Journal of Royal Statistical Society B, 51 no.1, pp. 61-69.

M.D. ERNST (1998). A multivariate generalized Laplace distribution. Computational Statistics 13, pp. 227-232.

FANG KAI-TAI, S. KOTZ, KAI WANG NG (1987). Symmetric multivariate and related distributions. Chapman & Hall. London.

D. GEORGE, S. GEORGE (2013). Marshall-Olkin Esscher transformed Laplace distribution and processes. Brazilian Journal of Probability and Statistics, forthcoming, vol.27, no.2 (2013), pp. 162-184.

K.K. JOSE, T. LISHAMOL, J. SREEKUMAR, (2008). Autoregressive processes with normal Laplace marginals. Statistics and Probability Letters 78, pp. 2456-2462.

K.K. JOSE, T. LISHAMOL, V. JILESH, K. JAYAKUMAR (2010). An AR(1) Time Series Model with Skew Laplace III Marginals. Journal of Statistical Theory and Applications 9, no. 3, pp. 417-416.

K.K. JOSE, M.T. MANU (2011). Generalized Laplacian distributions and autoregressive processes. Communications in Statistics-Theory and Methods 40, pp. 4263-4277.

K.K. JOSE, K.D. MARIYAMMA (2012). Integer valued autoregressive processes with generalized discrete Mittag-Leffler marginals. STATISTICA, 72, no. 2, pp. 195-209.

K.K. JOSE, M.T. MANU (2012). A product autoregressive model with log-Laplace marginal distribution. STATISTICA, 72, no. 3, pp. 317-336.

D. KELKER (1970). Distribution theory of spherical distributions and a location scale parameter generalization. Sankhya, Series A, 32, pp. 419-430.

T. KOLLO, M.S. SRIVASTAVA (2004). Estimation and testing of parameters in multivariate Laplace distribution. Communications in Statistics-Theory and Methods 33, no. 10, pp. 2363-2387. E. KRISHNA, K.K. JOSE (2011). Marshall-Olkin Generalized Asymmetric Laplace distributions and processes. STATISTICA 71, no. 4, pp. 453-467

Z.M. LANDSMAN, E.A. VALDEZ (2003). Tail conditional expectations for elliptical distributions. North American Actuarial Journal, 7, no. 4, pp. 55-122.

T. LISHAMOL (2008). Autoregressive processes with convolution of Gaussian and non-Gaussian stationary marginals. STARS: Int. Journal (Sciences) 2, no.1, pp.1-19.

T. LISHAMOL, K.K. JOSE (2009). Generalized normal-Laplace AR process. Statistics and Probability Letters, 79, pp.1615-1620.

T. LISHAMOL, K.K. JOSE (2010). A unified framework for Gaussian and non-Gaussian AR(1) modelling. Journal of Probability and Statistical Science, 8, no. 1, 97-105.

T. LISHAMOL, K.K. JOSE (2011). Geometric Normal-Laplace Distributions and Autoregressive Processes. Journal of Applied Statistical Science, 18, no. 1, pp.153-160.

K.V. MARDIA (1970). Measures of multivariate skewness and kurtosis with applications. Biometrical Journal, 31, pp. 619-624.

R.N. PILLAI (1990). Harmonic mixtures and geometric infinite divisibility. Journal of Indian Statistical Association, 28, pp.87-98.

W.J. REED, M. JORGENSEN (2004). The double Pareto lognormal distribution-a new parametric model for size distributions. Communications in Statistics-Theory and Methods, 33, no. 8, pp.1733-1753.

W.J. REED (2006). The normal-Laplace distribution and its relatives. Advances in Distribution Theory, Order Statistics, and Inference Statistics for Industry and Technology, Part II, pp. 61-74.

W.J. REED (2007). Brownian Laplace motion and its use in financial modelling. Communications in Statistics-Theory and Methods, 36, no.3, pp. 473-484.

C.H. SIM (1994). Modelling non-normal first order autoregressive time series. Journal of Forecasting, 13, pp. 369-381.




How to Cite

Jose, K. K., & Thomas, M. M. (2014). Multivariate normal-Laplace distribution and processes. Statistica, 74(1), 27–44.