An extended Lomax distribution

A new five-parameter continuous distribution, the so-called McDonald Lomax distribution, that extends the Lomax distribution and some other distributions is proposed and studied. The model has as special sub-models new four- and three-parameter distributions. Various structural properties of the new distribution are derived, including expansions for the density function, explicit expressions for the moments, generating and quantile functions, mean deviations and Rényi entropy. The score function is derived and the estimation is performed by maximum likelihood. We also obtain the observed information matrix. An application illustrates the usefulness of the proposed model.

[1]  I. Olkin,et al.  A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families , 1997 .

[2]  Amal S. Hassan,et al.  Optimum Step Stress Accelerated Life Testing for Lomax Distribution , 2009 .

[3]  P. Kumaraswamy.  A generalized probability density function for double-bounded random processes , 1980 .

[4]  S. Nadarajah.  Exponentiated Pareto distributions , 2005 .

[5]  T. Nayak.  Multivariate Lomax distribution: properties and usefulness in reliability theory , 1987, Journal of Applied Probability.

[6]  Narayanaswamy Balakrishnan,et al.  A General Purpose Approximate Goodness-of-Fit Test , 1995 .

[7]  Mohammad Ahsanullah,et al.  Record values of the Lomax distribution , 1991 .

[8]  F. A. Seiler,et al.  Numerical Recipes in C: The Art of Scientific Computing , 1989 .

[9]  K. Lomax.  Business Failures: Another Example of the Analysis of Failure Data , 1954 .

[10]  Elisa T. Lee,et al.  Statistical Methods for Survival Data Analysis , 1994, IEEE Transactions on Reliability.

[11]  Pushpa L. Gupta,et al.  Modeling failure time data by lehman alternatives , 1998 .

[12]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[13]  K. Song.  Rényi information, loglikelihood and an intrinsic distribution measure , 2001 .

[14]  Joseph Lipka,et al.  A Table of Integrals , 2010 .

[15]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[16]  F. Famoye,et al.  BETA-NORMAL DISTRIBUTION AND ITS APPLICATIONS , 2002 .

[17]  H. Howlader,et al.  Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data , 2002 .

[18]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[19]  Narayanaswamy Balakrishnan,et al.  Relations for single and product moments of record values from Gumbel distribution , 1992 .

[20]  C. Duarte,et al.  Some aspects of the analysis of size spectra in aquatic ecology , 1997 .

[21]  R. P. Gupta,et al.  Bivariate Extension of Lomax and Finite Range Distributions through Characterization Approach , 1996 .

[22]  M. E. Ghitany,et al.  Marshall–Olkin Extended Lomax Distribution and Its Application to Censored Data , 2007 .

[23]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[24]  Gauss M. Cordeiro,et al.  A new family of generalized distributions , 2011 .

[25]  M. C. Jones.  Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages , 2009 .

[26]  N. L. Johnson,et al.  Continuous Univariate Distributions. , 1995 .

[27]  Frank G. Garvan,et al.  The MAPLE Book , 2001 .

[28]  Saralees Nadarajah,et al.  Sums, products, and ratios for the bivariate lomax distribution , 2005, Comput. Stat. Data Anal..

[29]  Timothy A. Davis,et al.  MATLAB Primer , 1994 .

[30]  Elisa Lee,et al.  Statistical Methods for Survival Data Analysis: Lee/Survival Data Analysis , 2003 .

[31]  Constantinos Petropoulos,et al.  Improved estimation of extreme quantiles in the multivariate Lomax (Pareto II) distribution , 2004 .

[32]  Narayanaswamy Balakrishnan,et al.  Order statistics from non-identical right-truncated Lomax random variables with applications , 2001 .