Journal of Applied Statistics, Vol. 28, No. 8, 2001, 1051- 1065 A multivariate Gompertz-type distribution SAMIA A. ADHAM 1 & STEPHEN G. WALKER 2 , 1 Department of Mathematics, Imperial College London and 2 University of Bath, UK abstract The Gompertz distribution has many applications, particularly in medical and actuarial studies. However, there has been little recent work on the Gompertz in comparison with its early investigation. The problem of ®nding and analysing a bivariate (or multivariate) Gompertz distribution is of interest and the focus of this paper. A search of the literature suggests there is currently no multivariate or even useful bivariate Gompertz distribution. 1 Introduction The Gompertz distribution is one of the most important growth models. It has many applications in, for example, medical, biological and actuarial studies. In the early 19th century, the Gompertz mortality function was established by Benjamin Gompertz (1825), by supposing that If the average exhaustions of a man’s power to avoid death were such that at the end of equal in®nity small intervals of time, he lost equal portions of his remaining power to oppose destruction which he had at the commencement of those intervals, then at the age t his power to avoid death or the intensity of his mortality might be denoted by ace at ; a and c being constant quantities. A non-negative random variable T follows a Gompertz distribution with para- meters a and c, if its distribution function is given by: P(T < t) 5 F(t ½a, c) 5 1 2 e 2 c(e at 2 1) , t > 0( 2 ` < a, c < ` ) (1) Correspondence : S. G. Walker, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK. E-mail: massgw@bath.ac.uk ISSN 0266-4763 print; 1360-0532 online/01/081051-15 © 2001 Taylor & Francis Ltd DOI: 10.1080/02664760120076706