# Lloyd, E H

## Contents

## Photograph[edit]

Vit Klemes and Emlyn Lloyd in 1987

## Dates[edit]

Emlyn Howard Lloyd May 27, 1918 (Aberdare, Wales) - June 9, 2008 (Yealand Redmayne, Lancaster)

## Biography[edit]

Emlyn Howard Lloyd was born in 1918 in Aberdare, then a thriving town, part of the huge South Wales coal industry. His is an almost clichéd story of a beloved only child, son of an active trade union mining father and fervent chapel choir singing mother. Through their determination, his own intellectual ability and the schooling of Aberdare Grammar, Emlyn left the Welsh valleys to gain a first class honours degree in mathematics from the university of London in 1938. While he was still a student at Imperial College, very active in socialist politics, he met his wife, Herta, who was a refugee from Vienna. When bombed out of their Bloomsbury flat, they moved to the suburbs, becoming part of a large circle of emigrés and refugees. His four daughters were born there in the period 1942-56.

During the war years, Emlyn was employed by the Ordnance Board and the aircraft industry, and shortly after he was approached to join the staff of Imperial College by George Barnard, whom he knew through the London Labour Club. He took a doctorate on probability theory and mathematical statistics and embarked on his research career. Emlyn established a reputation in stochastic reservoir theory, and published definitively on the sensitivity of the reliability of storage to the various statistics of the input stream – a subject germane to water-challenged parts of Africa. He investigated the long-term properties of the statistics of river flows, and the so-called Hurst phenomenon, an early example of a fractal process. His name is still highly respected in hydrological science, though his work is now also frequently cited in financial journals because of its relevance to the long-range dependence of financial time series.

By the mid 1960’s it was evident to scientists studying the structure of paper that its physical properties were highly dependent on the statistical geometry of its fibres. As a consultant to Wiggins Teape, Emlyn developed with Heinz Corte, the theory that allowed papermakers to calculate the optimum uniformity that can be achieved in a sheet formed from fibres of a given type. The equations resulting form this pioneering research are still taught to students of paper technology around the world, and his work continues to be applied to new materials of fibrous networks.

In 1964 Emlyn left Imperial College to come to Lancaster as the founding professor of mathematics. With his courteous and charming manner, coupled with mental acuity, he was very active in university affairs, being principal of Lonsdale College from 1967 to 1982, and a member of the Senate and associated committees throughout his entire period of service at Lancaster. He retired from the university as professor emeritus in September 1982. Two of the academic disciplines of the department that he established, Mathematical Analysis and Statistics, continue to be its main strength. His personal qualities and eloquence of expression (though not his legibility of writing) were no doubt a factor in a successful bid during the 70’s, for a professorial fellow in applied statistics, funded by the Social Science Research Council. This required his co-ordination of research groups in a wide range of university departments and the legacy of this achievement is evident in many of the University’s present research strengths, including the standing of the statistics group among the top three in the country, which greatly pleased Emlyn in his later years.

## Hydrological Achievements[edit]

Emlyn's name became well known in hydrology through his pioneering work in stochastic reservoir theory where, in 1963, the 'Lloyd Model' extended the classical 'Moran Model' to handle serially correlated reservoir inflows. In 1967 he published his widely admired 60-page review article 'Stochastic Reservoir Theory' which, together with Moran's 1959 'The Theory of Storage', laid the foundations of the discipline in the English-speaking world. The work on storage problems aroused Emlyn's interest in the peculiar type of serial correlation of river flows that gave rise to the so-called Hurst phenomenon, a 'puzzle' that has challenged stochastic hydrologists for over half a century. Here Emlyn also made a lasting contribution with his papers on the distributions of cumulative sums, one of the problems at the root of this phenomenon. His work is now also frequently cited in financial journals because of its relevance to the long-range dependence in financial time series.

## Anecdotes[edit]

From the obituary by Vit Klemes:

"Having myself worked in reservoir analysis, I had been familiar with the Lloyd Model since its first appearance in the literature, but it was the 'Hurst phenomenon' that started my 34-year long friendship with Emlyn - the most rewarding 'side-effect' of my involvement in this 'controversial' matter. This gives me an opportunity to add a few personal notes on Emlyn.

Emlyn was a modest, kind and highly cultured man, with a sense of subtle good-natured humour. He never showed his intellectual superiority, never allowed his counterpart to feel inadequate and his criticism was subdued, usually offering some back door for escape to the offender. I have often benefited from his benevolence when, in response to some of my mathematical miss-steps he would merely note "I am not entirely happy with ...".

On the other hand, Emlyn was generous with praise which, even when sometimes laced with a tongue-in-cheek exaggeration, was always sincere. I still cherish a letter of his where, after our year-long correspondence about one Russian paper, he admitted to have wrongly suspected an error in one of its equations. It started "I hereby bestow upon you the Order of Wise Interpretation, First Class (Division of wising up ignorant probabilists). I now see that I have been criticising K for having had a different definition ..."

In the mid-nineties, I secured Emlyn's help in the assessment of extreme flood probabilities for the dam safety studies done by BC Hydro in which I was marginally involved. Emlyn's interest was captured by the practical urgency of the task and the problem kept him intellectually occupied for the rest of his life. To my surprise, his attitude was more realistic than that of many "practitioners". For instance, in one of his first letters on the subject he said "[in my last letter] I was casting doubt on the belief that the occurrences of very rare geophysical events such as catastrophically heavy rainfall could meaningfully be said to be subject to probability distributions. For events which are merely ordinarily rare, however, there is no doubt that there is a real problem of optimally estimating the (say) 1/100 exceedance value, since clearly probability theory IS applicable in such cases" (his emphasis). Pity that this doubt of a mathematician, who had spent over sixty years working with probability distributions and knew what he was talking about, is not shared by many practitioners who, to the contrary, usually seek from these distributions enlightment on the probabilities of such catastrophic events.

It was till 2006 that Emlyn used me as a bouncing board for his never ceasing new ideas about the above mentioned 'optimal estimations', thereby uncovering ever more of my mathematical inadequacies of which he has always been mercifully tolerant. Then his "energies", to use his word, started gradually to leave him and he only reminisced about the "glory days" of our intellectual exchanges.

In March 2007 Emlyn informed me in a touchingly philosophical letter about being diagnosed with cancer, not forgetting to apologize, as always when he did not use his old "steam" typewriter or e-mail, for his famously illegible handwriting. His last letter from early December 2007 was a passionate note accompanying the obituary of his beloved wife Herta for whom he cared with devotion while she was confined to a wheel-chair and who had died a month previously. He is survived by his four daughters, 9 grandchildren and 9 great grandchildren."

## Reference Material[edit]

## Major Publications[edit]

Lloyd, E.H., 1952. Least-squares estimation of location and scale parameters using order statistics. Biometrika, 39(1/2), pp.88-95.

Anis, A.A. and Lloyd, E.H., 1953. On the range of partial sums of a finite number of independent normal variates. Biometrika, 40(1-2), pp.35-42.

Lloyd, E.H., 1963. A probability theory of reservoirs with serially correlated inputs. Journal of Hydrology, 1(2), pp.99-128.

Lloyd, E.H., 1963. with Serially Correlated Inflows. Technometrics, 5(1), pp.85-93.

Lloyd, E.H., 1963. The epochs of emptiness of a semi-infinite discrete reservoir. Journal of the Royal Statistical Society. Series B (Methodological), pp.131-136.

Lloyd, E.H. and Odoom, S., 1964. Probability theory of reservoirs with seasonal input. Journal of Hydrology, 2(1), pp.1-10.

Lloyd, E.H. and Odoom, S., 1964. A note on the solution of dam equations. Journal of the Royal Statistical Society. Series B (Methodological), pp.338-344.

Odoom, S. and Lloyd, E.H., 1965. A note on the equilibrium distribution of levels in a semi-infinite reservoir subject to Markovian inputs and unit withdrawals. Journal of Applied Probability, 2(1), pp.215-222.

Lloyd, E.H., 1967. Stochastic reservoir theory. Advances in hydroscience, 4, pp.281-339.

Anis, A.A. and Lloyd, E.H., 1972. Reservoirs with mixed Markovian-independent inflows. SIAM Journal on Applied Mathematics, 22(1), pp.68-76.

Lloyd, E.H., 1974. What is, and what is not, a Markov chain?. Journal of Hydrology, 22(1-2), pp.1-28.

Anis, A.A. and Lloyd, E.H., 1975. Skew inputs and the Hurst effect. Journal of Hydrology, 26(1-2), pp.39-53.

Annis, A.A. and Lloyd, E.H., 1976. The expected value of the adjusted rescaled Hurst range of independent normal summands. Biometrika, 63(1), pp.111-116.

Anis, A.A., Lloyd, E.H. and Saleem, S.D., 1979. The linear reservoir with Markovian inflows. Water Resources Research, 15(6), pp.1623-1627.

Lloyd, E.H. and Saleem, S.D., 1979. A note on seasonal Markov chains with gamma or gamma-like distributions. Journal of Applied Probability, 16(1), pp.117-128.