**Arnljot Høyland**was a mathematical statistician. His parents were Torleiv Høyland (1893-1989), a teacher, and Sigyn Tønnesdtr Husebø (1899-1994), a clerk. Arnljot was one of his parents' three children. Torleiv Høyland was the author of the book

*Laerernes Kirkenesferd*Ⓣ (1946). This book was about something that happened in 1942, when many school teachers were sent to a labour camp in Kirkenes, a small city in the North of Norway, next to Russia, for refusing to introduce Nazi ideology into schools. Torleiv Høyland was prisoner no 1850 there.

Arnljot Høyland is internationally renowned for his work in mathematical statistics. He has been a very active participant in the development of statistics in Norway, including as a textbook author. He is also known for having composed, in 1944, the melody of Alf Prøysen's "Julekveldsvise," a very famous Norwegian Christmas song. Høyland met Alf Prøysen, a famous Norwegian writer and musician, during the last years of the war. They cooperated among other things on shows, and it was in this context that Høyland composed the melody Prøysen later used in his "Julekveldsvise". Because if this Høyland was interviewed several times on Norwegian television in the 1990s.

Høyland completed his high school studies and took his matriculation examination in 1943. In April 1940 German troops invaded Norway and on 1 May the Norwegians surrendered. At this time Høyland was a sixteen year old schoolboy. The following years were difficult with the German occupation of Norway. However, Høyland completed his high school studies and took his matriculation examination in 1943. He intended to begin his university studies at the University of Oslo in the autumn of 1943 but this proved impossible at that time. The Germans had attempted to convert the university to the Nazi philosophy but, when this was unsuccessful, they closed down the University of Oslo on 30 November 1943. He had to put off time for two years until the war had ended.

At the end of the war, in autumn 1945, Høyland began to study at the University of Oslo. He planned to study mathematics, mechanics, chemistry and physics, with physics as his major subject. However, after starting his course, he was told that those born in 1924 were required to do three months military service. He went to the War Commission in Oslo and asked if he could do his military service over the summer of 1946 so that he could continue his university studies in the autumn of that year. He was told that they needed two recruits in the Armed Forces High Command and he was told to speak to them. When he arrived at the indicated place, he discovered it was the Intelligence Service of the Norwegian Defence. He was interviewed by the head of the service, Erling Sverdrup (1917-1994), a statistician who had been involved in the fighting in Norway during World War II. Høyland was given some tests and then told he could start work. The second person appointed was Harald Bastiansen who later became director of the Municipal Land Fund. They were given the task of solving 26 equations in 26 unknowns. They spent much of the summer of 1946 working on this problem. The number 26 came from the fact that there were 26 letters in the alphabet.

Towards the end of his three months, he was asked if he would stay on until the end of the year and be made a second lieutenant. Høyland needed the money, so he accepted. He left the Intelligence Service on 1 January 1947 and returned to his studies at the University of Oslo. However, in the autumn of 1947 he was asked if he would apply for the position of captain in the army, attached to the Intelligence Service. He submitted an application and he became a captain in 1948. He received a little military training at the Huseby military camp, being shown how to fire a gun. Beginning in March 1948, he was given the task of building up an analysis department of the Norwegian Defence consisting of mathematicians and linguists, where he quickly became aware of the necessity of learning statistics. This led to his mathematics studies at university, which Høyland completed while holding his position in the Intelligence Service, having a high component of mathematical statistics. He took courses on mathematics, mechanics and chemistry during 1947, 1948 and 1949. Although he knew he needed to learn statistics, the subject was not taught as part of the Mathematics and Natural Sciences degree at the University of Oslo at this time. Together with a fellow student, he talked to the university professors, Thoralf Skolem, Ingebrigt Johansson (1904-1987) and Ralph Tambs-Lyche (1890-1991) and asked them what they should do.

The results of these discussions were that Johansson agreed that they could drop geometry, and Skolem agreed that they could also drop algebra and number theory. They were to take function theory, based on Konrad Knopp's book *Elemente der Funktionentheorie* Ⓣ, and analysis based on Edouard Goursat's book *Cours d'analyse mathématique* Ⓣ. To cover the statistics that they wanted, they were to read the statistics book *Introduction to the theory of statistics* by Alexander McFarlane Mood (1913-2009), and Harald Cramér's book *Mathematical Methods of Statistics*. In addition Olav Reiersøl (1908-2001) would give some special lectures on statistics and give them a topic for a thesis. Reiersøl suggested a topic on probability densities of specific differential equations. They had a difficulty with Reiersøl, however, since he was interested in the international language Esperanto and he was one of the founders of the International Association of Esperantist Mathematicians. He had written the works in Esperanto which Høyland had to read. Describing his thesis, Høyland said [3]:-

He was awarded his cand.real. degree (equivalent to a Ph.D.) after defending his thesis in the autumn of 1952. He then returned to his position in the Intelligence Service.... there was very little use of statistics. The differential equation took a whole page and so was utterly awful. But I got there. I was not so deeply concerned about what it could be used for, other than a thesis. It is a good job that nobody other than Reiersøl went thoroughly through the work.

On 20 October 1951, he had married had the statistician Liv Sirum, who was the daughter of chief engineer Esten Sirum (1889-1958) and Helga Amundsen (1901-1996).

As to his work with the Intelligence Service, Høyland says that 1948 was an exciting year. International moves were being made to establish NATO while the Norwegian Intelligence Service tracked Russian ships going in and out of international waters between the Kola Peninsula and the Baltic Sea [3]:-

Although he was working as a statistician, he still had military duties [3]:-They were plotted and followed throughout. For all we knew, they could suddenly turn around and go straight for us, as the Germans had done in1940.

Høyland retired from the Norwegian Defence in 1954, having attained the rank of a major. He then became a research assistant for Professor Erling Sverdrup at the University of Oslo and played an important part in establishing the new statistics subject. Sverdrup had been appointed as professor of mathematical statistics at the University of Oslo in 1953. However, Høyland's move was a costly one financially [3]:-We had offices under Akershus Fortress, just below the royal burial chapel. The building was secured with an alarm, and if someone broke in, the alarm went off. If that happened, you had to notify the duty officer. Then he would come out with a gun. When the alarm went off, most often middle of the night, we had to go on duty throughout the building to find out what it was. If we discovered someone who was about to break in, we would first shout, then shoot them in the legs. For a civilian like me this was fairly brutal. Fortunately I never discovered any intruders. In winter it was sometimes very cold, and I think that some of the alarms were triggered by temperature fluctuations.

At first he taught statistics within the mathematics department but, after about a year, statistics was accepted by the Faculty as a discipline in its own right. This was only achieved with difficulty since some, as for example the theoretical physicist Egil Hylleraas (1898-1965), argued that if anyone needed to use statistics they could learn all they need to know in an afternoon.As a Major I had reached salary grade17, which at that time was pretty good. As a research assistant, I went down to salary grade10. It had certainly never happened before in the State that someone had gone down so much, if they had not been dismissed. But I said yes and began as a research assistant in the autumn of1954. Now when I tell someone that I was in the military while studying most people seem to think that the military only funded me, and that I could study full time, but this was not so. I had to work fully for the reward I got.

In the autumn of 1957, funded by a scholarship from the Norwegian Technological Research Council, he went to the University of California, Berkeley, to begin studying at the prestigious statistics institute there. David Blackwell was head of statistics at that time and he advised Høyland to register as a Ph.D. student. He took a course on probability given by Michel Loève (1907-1979) and a course on hypothesis testing given by Erich Leo Lehmann (1917-2009). Lehmann was using the lectures he was giving as the basis for his famous book *Testing Statistical Hypotheses* (1959) and Høyland received a "thanks" in the Preface to the book for having worked through all the problems. He had only partially completed work on his Ph.D. thesis when he returned to Oslo in 1959.

Back in Oslo he began teaching and struggled to complete the work for his Ph.D. thesis. He applied to the Norwegian Technological Research Council for a second scholarship to allow him to return to California to complete the work for his Ph.D. He was successful and he returned to California in the autumn of 1962. He was told that the topic he had been working on three years earlier was now not suitable for a thesis since publications had appeared making the work obsolete. Writing a new thesis in a short time was difficult for he was supposed to return to Oslo to teach in the autumn semester of 1963. However, he managed to obtain extended leave and submitted his thesis *Some Problems in Robust Estimation* in August 1963. He received his PhD degree in late 1963 and returned to Oslo to begin teaching on 1 January 1964. Later, he became a key contact for other young Norwegians who wanted to do their PhD studies in the United States.

Back in Norway, Høyland had difficulties because he was arguing for non-parametric statistics. He said [4]:-

He had many battles with Scandinavian colleagues over this issue [4]:-In parametric theory often assumptions in the models are introduced exclusively to make it mathematically convenient.

Anders Hald (1913-2007) was professor at the University of Copenhagen from 1960.Sverdrup has always been very sympathetic to me, even though we were not always in complete agreement. ... Most Danish statisticians, except Anders Hald, protested against the philosophy of the non-parametric models.

After working as a lecturer at the University of Oslo from 1959 to 1965, Høyland was hired by the Norwegian Institute of Technology (NTH) in Trondheim as a senior lecturer in 1965 and later became a professor of mathematical statistics. At NTH he again had battles over his view of statistics [4]:-

Høyland was the first person who specialised in statistics that NTH hired. He had difficulties persuading others about the need for a specialised statistics course. He gave an example in [4]:-When I arrived there in January1965, there was no particular interest there for the non-parametric view. The engineers were making all sorts of measurements, and they thought that they really knew what kind of size measurements represent.

After strenuous efforts, he received approval for a separate course in statistics within all NTH engineering departments. During this time, his wife Liv, who became a lecturer in statistics at NTH in 1968, was a great help. Høylands 2-volume textbookWhen I came to Trondheim, I would visit the various departments, and I walked around with the mathematics professor John Olav Stubban(1909-1994)who introduced me. We came to the Chemistry Department. There I was very enthusiastic about how useful a statistics course would be in industrial chemistry. I did not know so much about the uses, but I took a chance. Among the chemistry staff sat an elderly gentleman who smoked a cigar. I had no idea who he was. When I had finished my mission lecture, he stood up and said that he understood that this could be interesting, especially in industrial chemistry. But within his own area, which was organic chemistry, one would never need to use something like that, because they never had so many observations that could apply statistics. Although I was young and enthusiastic, I should perhaps have been a little more careful. The man with the cigar was in fact a very significant person in the NTH environment, Professor Nils Andreas Sørensen. I jumped up and said it was the stupidest thing I had ever heard. It was precisely when one had little data that one needed to use statistical methods. If one had very many observations, even an idiot could draw the right conclusions, I suggested. He blushed, but said nothing more then.

*Sannsynlighetsregning og statistisk metodelaere*Ⓣ, published in 1972-73, was compulsory reading for the students at NTH for over 20 years. He remained there as a professor until 1990 and then as a senior researcher until 1994.

Through his contact with the statistics community in Berkeley, Høyland became familiar with the field of system reliability theory during the mid-1970s [8]:-

Høyland and Rausand were co-authors of an international textbookIn1975-76, Professor Arnljot Høyland, Department of Mathematical Statistics, had a sabbatical year at University of California, Berkeley, USA. Here he met Professor Richard E Barlow who had just published the seminal book "Statistical Theory of Reliability and Life Testing"(1975). When professor Høyland returned to NTNU(NTH at that time), he was very enthusiastic and wanted to start a course in reliability analysis at NTNU, using the book by Barlow and Proschan. He therefore asked Dr Bent Natvig to prepare a weekly seminar on this topic during the spring semester of1977. Bent Natvig stayed only a short time and left NTNU during the summer of1977- so when the first ordinary course in reliability analysis was to be lectured, professor Høyland had to be the lecturer - with assistance from Marvin Rausand who took over Bent Natvig's position as an assistant professor.

*System Reliability Theory: Models and Statistics Methods*(1994). You can read extracts from the Preface and from some reviews of the book at THIS LINK.

You can read Høyland and Rausand's *Brief History of Reliability* at THIS LINK.

Høyland was known for his cheerful spirit and his musicality. He has always been perceived as a community builder, a characteristic that has undoubtedly had an impact on his achievements. Over the years, he set up an extensive network among academics worldwide.

Arnljot Høyland was appointed Knight of First Class of the Order of St Olav in 1995. He has been a member of the Norwegian Academy of Technological Sciences since 1972, the Royal Norwegian Academy of Sciences and Letters since 1975 and the International Statistical Institute since 1966.

**Article by:** *J J O'Connor* and *E F Robertson*