# Ernest Enns

#### Professor Emeritus of Mathematics & Statistics

#### PhD

#### BSc

## Contact information

#### Phone

#### Location

## Research and teaching

### Research interests

- Stochastic geometry; distributions of the lengths of random secants and rays in n-dimensional convex regions generated in one region and terminating in another;
- Decision theory: investigation of optimal strategies in sequential decision problems extended to multiple players and the problem is reformulated in terms of game theory
- Operations research

## Publications

### Book

*Enns, Ernest*. Dependence relationships for rays in a convex body in {${\bf R}\sp n$} 16. Inst. Math. Statist., 1990. 203-206. Print.*Enns, Ernest, Ehlers, Peter and Stuhr, Stein*. Every body has its moments 79. Reidel, 1981. 387-396. Print.

### Journal Article

*Ehlers, Peter, Enns, Ernest and Fung, Tak*. "Rectilinear and {B}rownian motion from a random point in a convex region". Image Analysis \& Stereology. Official Journal of the International Society for Stereology 20.2 (2001): 113-117. Print.*Enns, Ernest*. "Finding the volume of a mountain using stereological methods". Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento, 65, part I (2000): 117-120. Print.*Enns, Ernest, Ehlers, Peter and Misi, T.*. "A cluster problem as defined by nearest neighbours". The Canadian Journal of Statistics 27.4 (1999): 843-851. Print.*Enns, Ernest and Tomkins, D. D.*. "Optimal betting allocations". The Mathematical Scientist 18.1 (1993): 37-42. Print.*Enns, Ernest and Ehlers, Peter*. "Notes on random chords in convex bodies". Journal of Applied Probability 30.4 (1993): 889-897. Print.*Ravindran, K. and Enns, Ernest*. "A two {P}oisson stream competitive decision problem". Mathematica Japonica 37.4 (1992): 723-731. Print.*Enns, Ernest and Ferenstein, E. Z.*. "A competitive best-choice problem with {P}oisson arrivals". Journal of Applied Probability 27.2 (1990): 333-342. Print.*Ferenstein, E. Z. and Enns, Ernest*. "Optimal sequential selection from a known distribution with holding costs". Journal of the American Statistical Association 83.402 (1988): 382-386. Print.*Enns, Ernest and Ehlers, Peter*. "Chords through a convex body generated from within an embedded body". Journal of Applied Probability 25.4 (1988): 700-707. Print.*Enns, Ernest and Ferenstein, E. Z.*. "On a multiperson time-sequential game with priorities". Sequential Analysis 6.3 (1987): 239-256. Print.*Enns, Ernest, Ferenstein, E. and Sheahan, J. N.*. "A curious recursion arising in game theory". Utilitas Mathematica. A Canadian Journal of Applied Mathematics, Computer Science, and Statistics 30. (1986): 219-228. Print.*Enns, Ernest and Ferenstein, E.*. "The horse game". Journal of the Operations Research Society of Japan 28.1 (1985): 51-62. Print.*Enns, Ernest, Smith, B. R. and Ehlers, Peter*. "Hitting spheres with straight-line motion or {B}rownian motion". Journal of Applied Probability 21.1 (1984): 70-79. Print.*Ehlers, Peter and Enns, Ernest*. "Random secants of a convex body generated by surface randomness". Journal of Applied Probability 18.1 (1981): 157-166. Print.*Enns, Ernest and Ehlers, Peter*. "Random paths originating within a convex region and terminating on its surface". The Australian Journal of Statistics 22.1 (1980): 60-68. Print.*Enns, Ernest and Ehlers, Peter*. "Random paths through a convex region". J. Appl. Probability 15.1 (1978): 144-152. Print.*Enns, Ernest and Ehlers, Peter*. "Optimal issuing policies for non-identical units with stochastic lifetimes". J. Appl. Probability 13.1 (1976): 183-189. Print.*Enns, Ernest*. "Correction to: ``{T}he decision process for maximizing the probability of obtaining the random variable nearest to an arbitrary real number'' ({A}nn. {M}ath. {S}tatist. {\bf 41} (1970), 1466-1471)". Ann. Statist. 1. (1973): 400. Print.*Enns, Ernest*. "The distributions of a number of random variables associated with the absorbing {M}arkov chain". The Australian Journal of Statistics 14. (1972): 79-83. Print.*Enns, Ernest*. "Reply to {M}. {J}. {B}eckmann's ``{N}ote on: {T}he optimum strategy for choosing the maximum of {$N$} independent random variables''". Unternehmensforschung 15. (1971): 60-61. Print.*Enns, Ernest*. "The decision process for maximizing the probability of obtaining the random variable nearest to an arbitrary real number". Ann. Math. Statist. 41. (1970): 1466-1471. Print.*Enns, Ernest*. "The optimum strategy for choosing the maximum of {$N$} independent random variables". Unternehmensforschung 14. (1970): 89-96. Print.*Enns, Ernest*. "The trivariate distribution of the maximum queue length, the number of customers served and the duration of the busy period for the {$M/G/1$} queueing system". J. Appl. Probability 6. (1969): 154-161. Print.