Moshe Shaked, a leading figure in stochastic orders and distribution theory, died unexpectedly on October 28, 2014, in Tucson, Arizona, at the age of 69. Shaked is survived by his wife of 37 years, Edith; his son Tal; his two daughters, Shanna and Lila; his daughter in law, Carrie; his son-in-law, Jasper; and two grandchildren, Zinnia and Zia. He is also survived by his sisters Tamar Sarid, Anat Weiner, his niece Iris Ginzburg, and his nephew Tal Ginzburg.

Moshe Shaked was born on February 21, 1945 in Jerusalem, Israel. His parents immigrated to British Mandate of Palestine from Poland in 1936; the rest of the family remained there and died in the Holocaust in occupied Poland during World War II. Moshe attended the Hebrew University of Jerusalem and received BA cum laude in 1967, and MA in 1971. As a student he was quiet, smiling a lot, but rather critical and skeptical of many things, from statistics to politics, as he was throughout his career. Moshe pursued his graduate studies in statistics at the University of Rochester from 1971 to 1975. He received his PhD in statistics under the supervision of Albert W. Marshall in 1975 with a thesis entitled, On Concepts of Positive Dependence. After short stays at the University of New Mexico, University of British Columbia and Indiana University, Moshe became an associate professor of mathematics at the University of Arizona in 1981, then, in 1986, a full professor at the same institution, where he remained until his retirement in May 2013, when he became a Professor Emeritus.

Moshe Shaked is world-renowned for his work in applied probability and statistics. He published over 180 papers and three books. Most of the research papers and the books were written jointly with one or more coauthors from a list of over 60 collaborators from all over the world, including some of the most prominent probabilists and statisticians of the era. He became most celebrated internationally for his collection of influential papers on stochastic orders and multivariate dependence. Stochastic ordering refers to comparing random elements in some stochastic sense, and has evolved into a deep field of enormous breadth with ample structures of its own. An early study on stochastic orders involving convex functions can be traced back to the work of the Serbian mathematician Jovan Karamata in 1932. The systematic studies on stochastic orders and their applications to various areas have been intensified since the 1960s, most notably by researchers with interests in reliability theory and queueing theory, and more recently by researchers working in financial risk management. Moshe Shaked’s books on stochastic orders, coauthored with George Shanthikumar, became instant influential classics in the field. The analysis of stochastic orders and exploitation of their deeper properties often lead to breakthroughs in deriving sharp probability inequalities, analyzing dispersion and concentration of probability measures, establishing performance comparison of complex stochastic systems, characterizing stochastic dependence, etc. The growing applications of stochastic orders in statistics, operations research, and risk analysis might not have happened without the advocacy and persistence of Moshe and his colleagues.

Shaked’s bibliography also includes pioneering studies on stochastic convexity and on multivariate phase-type distributions, with important applications in reliability modeling and queueing analysis. He made significant contributions to multivariate aging notions and multivariate life distributions, as well as accelerated life tests (inference, non-parametric approach and goodness of fit). Moshe Shaked’s interests and contributions are extremely broad; for example, he made a seminal contribution to analyzing scientific activity and truth acquisition in social epistemology.

Moshe Shaked was elected an IMS Fellow in 1986, and served since 1994 on the editorial boards of several probability and statistics journals. Moshe was invited to speak and lecture at numerous international conferences, and he and his wife Edith traveled together a lot professionally. His university retirement did not slow him down, socially or academically; in the summer of 2014, Moshe Shaked and Edith visited Poland for the first time and he delivered a plenary talk at a conference on ordered statistical data in Poznań, sponsored by the Stefan Banach Center.

Throughout his career, Moshe Shaked exemplified the highest standards of scholarship and professionalism. For collaborators, he was generous and accommodating; for his students, he was an inspiring friend. Moshe was an ancient coin enthusiast, a passionate museum-goer, and he was a man of high culture, who also respected and appreciated cultures other than his own. He will be deeply missed by his many colleagues, coauthors, students, and by his family.

Written by Haijun Li, Washington State University, and George Shanthikumar,
Purdue University