mathematics

Ingram Olkin

Ingram Olkin is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Ingram Olkin rather than just read about it. In short: Ingram Olkin (July 23, 1924 – April 28, 2016) was a professor emeritus and chair of statistics and education at Stanford University and the Stanford Graduate School of Education. He is known for developing statistical analysis for evaluating policies, particularly in education, and for his contributions to meta-analysis, statistics education, multivariate analysis, and majorization theory.

Key takeaways

Ingram Olkin belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Ingram Olkin to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Ingram Olkin from memory before moving on to harder problems.

Reference excerpt

Ingram Olkin (July 23, 1924 – April 28, 2016) was a professor emeritus and chair of statistics and education at Stanford University and the Stanford Graduate School of Education. He is known for developing statistical analysis for evaluating policies, particularly in education, and for his contributions to meta-analysis, statistics education, multivariate analysis, and majorization theory.

Biography Olkin was born in 1924 in Waterbury, Connecticut. He received a B.S. in mathematics at the City College of New York, an M.A. from Columbia University, and his Ph.D. from the University of North Carolina. Olkin also studied with Harold Hotelling. Olkin's advisor was S. N. Roy and his Ph.D. thesis was "On distribution problems in multivariate analysis" submitted in 1951. Olkin died from complications of colorectal cancer at his home in Palo Alto, California on April 28, 2016, aged 91.

Honors and awards Olkin was awarded the fourth biennial Elizabeth Scott Award in 1998 from the American Statistical Association for his achievements in supporting women in statistics. Of the 17 recipients thus far, he is the only man. In 1962 he was elected as a Fellow of the American Statistical Association. In 1984, he was President of the Institute of Mathematical Statistics. In 1991 Olkin was awarded the American Statistical Association's Founders Award. Olkin is a Guggenheim, Fulbright, and Lady Davis Fellow, with an honorary doctorate from De Montfort University.

Publications and editing Olkin has written many books including Statistical methods for meta-analysis, Probability theory, and Education in a Research University. Olkin's coauthors include S. S. Shrikhande and Larry V. Hedges. Olkin has written two books with Albert W. Marshall, Inequalities: Theory of Majorization and its Applications (1979) and Life distributions: Structure of nonparametric, semiparametric, and parametric families (2007). In nonparametric statistics and decision theory, Olkin wrote Selecting and ordering populations: A new statistical methodology with Jean Dickinson Gibbons and Milton Sobel (1977, 1999). Ingram was Editor of the Annals of Mathematical Statistics and served as the first editor of the Annals of Statistics, both published by the Institute of Mathematical Statistics. He was a primary force in the founding of the Journal of Educational Statistics, which is published with the American Statistical Association. Olkin was also an editor with the mathematics journal, Linear Algebra and its Applications, and has been active in supporting a series of international conferences on matrix theory, linear algebra, and statistics.

Bibliography Golbeck, Amanda L.; Olkin, Ingram; Gel, Yulia R., eds. (2015). Leadership and Women in Statistics. Chapman & Hall/CRC Press. ISBN 978-1482236446. Hedges, Larry V.; Olkin, Ingram (1985). Statistical methods for meta-analysis. Boston: Academic Press. ISBN 978-0-12-336380-0. Marshall, Albert W.; Olkin, Ingram (1967), "A multivariate exponential distribution", Journal of the American Statistical Association, 62 (317): 30–49, doi:10.2307/2282907, JSTOR 2282907, MR 0215400 Inequalities: Theory of Majorization and Its Applications (2011) Albert W. Marshall, Ingram Olkin, Barry Arnold, Springer, ISBN 978-0-387-40087-7 Inequalities: Theory of Majorization and Its Applications (1979) Albert W. Marshall, Ingram Olkin, Academic Press, ISBN 978-0-12-473750-1 "A Guide to Probability Theory and Application" (1973), with L. Gleser and C. Derman, Holt, Rinehart and Winston. "Probability Models and Application" (1994), with L. Gleser and C. Derman, Prentice Hall. A tribute to Marshall and Olkin's book "Inequalities: Theory of Majorization and its Applications"

References

External links Ingram Olkin – staff webpage at Stanford University (archived) Ingram Olkin at the Mathematics Genealogy Project Ingram Olkin

See also Marshall–Olkin exponential distribution

Illustrations

Worked examples

Example 1 — a first encounter with Ingram Olkin

Start with the simplest possible case. Write down what Ingram Olkin claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Ingram Olkin before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Ingram Olkin ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Ingram Olkin

In research: Ingram Olkin appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Ingram Olkin in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Ingram Olkin is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1924 births, 2016 deaths, 20th-century American social scientists, so understanding it makes those chapters shorter.
In everyday life: Look for Ingram Olkin outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Ingram Olkin in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ingram Olkin means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Ingram Olkin out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ingram Olkin in simple terms?

Why does Ingram Olkin matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ingram Olkin?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ingram Olkin.