Questions tagged [statistics]

For questions about the science that deals with classification, analysis and interpretation of numerical facts and data.

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48 views

How did percolation theory come to be established in network science, and who first studied it?

According to the textbook "Network Science" by Albert-László Barabási, percolation theory is a specialized branch of both mathematics and physics [1]. It involves node clustering in a ...
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57 views

Why is William Playfair seldom heard about in mathematics?

William Playfair was a Scottish engineer and economist, who invented the pie and bar charts as well as the line graph, which have all played an indubitably ubiquitous role in modern statistics. I hadn'...
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67 views

How was mathematics used in World War II to “act on the right amount of intelligence”?

In the movie "The Imitation Game", Alan Turing along with his team crack the German encryption machine Enigma but advises his superiors to not act on all decrypted intelligence, as that might lead to ...
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1answer
125 views

Why is a time series not called a time sequence?

In pure mathematics, a sequence is a list of terms, for instance $1, \frac12, \frac14, \dots, \frac{1}{2^k},\dots$, and a series is the sum of an infinite sequence, for instance $\sum_{k=1}^\infty \...
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1answer
87 views

Significance level $\alpha$ values - who devised to use $\alpha = 5 \%$?

In a statistical hypotheses testing a significance level $\alpha$ has to be set. The most often, $\alpha$ is set to be 5 %, sometimes 1 % and 10 % values are used. Value of $\alpha$ tells us what is ...
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206 views

Quotation about $\pi$ and the number of deaths

I read more than once a story which took place, if memory serves me well, in England, in the XIXth century. A statistician (or a mathematician) was making computations about life expectancy (or ...
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1answer
84 views

How did Weibull derive the three parameter Weibull distribution?

How did Weibull or any other mathematician arrive at the above expression? I saw the 1951 paper, but it is not clear to me. In 1939 he had published a book called "A Statistical Theory of the Strength ...
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1answer
110 views

Where does $M$ for expected value in Russian papers come from?

In modern papers in statistics, it is common to use the symbol $E[X]$ to refer to the expectation of a random variable $X$. While reading (a translated version of) "Convergence Rate of Nonparametric ...
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1k views

Why do many names of technical and scientific subjects end with “ics”?

The names of many technical and scientific subjects, like mathematics, physics, statistics, etc., etc., end with letters "ics". What is meant by this, if anything? Was there any logic behind it or is ...
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140 views

How is the word kernel associated with distributions?

I am trying to rationalize the meaning of the term kernel, especially when it is associated with distributions. The English and German etymology all show that the literal meaning is corn (English) and ...
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Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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1answer
68 views

Where did the story about Newcomb observing Benford’s Law come from?

The story goes that in the 1880s Newcomb noticed that logarithm tables were more worn down towards the beginning of the book (where the leading digit of the logs were 1). This led him to formulate an ...
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109 views

How did Quetelet discover that the body mass is proportional to the squared height?

The Body Mass Index (BMI) compares body masses on the assumption they scale with height squared, not cubed, an example of allometry. BMI is due to Lambert Quetelet. Why did he settle on this power law?...
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57 views

Who came up with a number of the theoretical plates equation?

In chromatography, the signal is shaped like a Gaussian peak, and it is plotted against time vs. instrument's signal. https://en.wikipedia.org/wiki/Chromatography#/media/File:Rt_5_12.png (a) One of ...
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1answer
65 views

Real effects long thought to be coincidences

What examples are there of scientific effects or correlations that we now know to be real, and were known about for a long time but thought to be coincidences? To give an example of the kind of thing ...
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351 views

What is the etymology of the term “mode” in statistics?

I saw that the word "mode" means "popular" in French, and I was wondering if this might be the etymology of the "mode" of a population in stat? I was wondering if anyone had sources for early use of ...
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264 views

Why statistical moments are called moments?

According to the Jeff Miller's Earliest Known Uses of the Words of Mathematics "Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
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55 views

Statistical Power as a Microscope Metaphor

An answer on this question on the cross validated stack exchange compared statistical power to a microscope, such that "in order to see small things you need a powerful microscope" is analogous to "in ...
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133 views

Law of the Unconscious Statistician - history of the term?

The "Law of the Unconscious Statistician" states that, for a random variable $X$ with density $f_X(x)$ and a function of it $h(X)$ we have that $$E[h(X)] = \int_{-\infty}^{\infty} f_X(x)h(x) dx$$ ...
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92 views

What is Peirce doing in this pre-Chi-squared example?

In 1878, C. S. Peirce performed a calculation that (I think) would be better done using chi-squared testing — but Pearson hasn’t introduced that yet. What exactly is Peirce doing here in the last ...
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113 views

How was the idea of observation error introduced?

The first thing a contemporary student of physics learns is the measurement error. As far as I understand, the idea of imprecision was totally foreign to natural philosophers at least until the end of ...
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105 views

Historical development of role of astrology in medicine?

The OED defines "iatromathematics" as Practising medicine in conjunction with astrology. Pre-17th century, it seems most scientists (physicians included) believed in the influence of the stars on ...
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207 views

Galileo and normal distribution discovery

If differential equation theory was known and also studied by Galileo, so why he didn't manage to discover a normal distribution (its discovery had to wait for Laplace and Gauss)?
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232 views

What defines the 'name' of a score i.e. gamma, kappa etc

I was just wondering if there is a process or set of properties that exist to name a score, such as, Cohen’s Kappa, Fleiss’ Kappa, Krippendorff’s Alpha, or if it is just at the creators choice. ...
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85 views

When did error propagation become prominent in physics?

I think is well known that greek scientists and even founding fathers of modern science did not use error propagation in their calculations. Today, instead, is unacceptable to work out any prediction ...
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Raymond Cattell and History of Personality Traits Prior 1947

I find that papers reference Raymond Cattell suggesting 16 or 22, etc, traits, by factor analysis (basically regression), including all five of the modern reproducible traits (openness to experience, ...
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Origin of diagrammatics illustrating the relation between cumulants and moments?

The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments. Who were some of the first to ...
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91 views

Why do we often minimize in optimization?

Because of the following relation, \begin{equation*} \inf(S) = -\sup(-S), \end{equation*} minimization and maximization is essentially the same thing. However, take any optimization routine in R for ...
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570 views

Who developed Gaussian Mixture Model (GMM) and applied it to machine learning?

I searched about GMM (Gaussian mixture model), but only found that normal distribution was invented by Carl Friedrich Gauss. I'd like to know who contributed to the development of GMM itself, and to ...
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1answer
80 views

Name and history of probabilistic non-inevitability paradox?

A counterintuitive result in probability theory that may warrant the description of a veridical paradox is the fact that repeating an experiment with a nonzero chance of success infinitely often does ...
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4k views

Hypothesis testing: Fisher vs. Popper vs. Bayes

I try to make my question short. I am familiar with Popper’s philosophy as well as with statistical hypothesis testing after Fisher and Neyman-Pearson. I am not so familiar with the Bayesian approach ...
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160 views

Secular Status Difference Between Applied and Pure Mathematics

Coming from outside the field but with healthy curiosity I have been struck by what may be regarded as a discrepancy between the impact on science at large of the mathematics developed in the field of ...
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Why do we see the modern version of regression as “Fisher's regression”?

In Fisher's paper, he did not include the error term. http://psychclassics.yorku.ca/Fisher/Methods/chap5.htm But Durbin & Watson suggested the error term, and also made the matrix form of the ...
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First usage of binomial distribution

As stated in the article binomial distribution by britannica.com the binomial distribution was used by Jakob Bernoulli when he said that "the probability of $k$ ... outcomes in $n$ repetitions is ...
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1k views

Where does Markov operator come from?

I found this definition of "Markov operator" in the book Chaos, Fractals, and Noise by Lasota and Mackey. Denote by $L^1(\mu)$ the space of Lebesgue integrable functions according to the measure $\mu$...
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Who introduced random variables into probability?

I used to think that the answer is Kolmogorov. So the Shafer-Vovk's review of Kolmogorov's famous 1933 axiomatization of probability surprised me a bit:"Today, what Frechet and his contemporaries knew ...
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218 views

construct for h-index and Eddington number

There is a construct very useful to measure the efficiency taking into account both quantity and quality, which states something like N is the highest number that fulfils the statement "in this set, ...
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On the history of population dynamics of territorial species

I am interested in the historical priority in population biology, essays or monographs, discussing the concept of territoriality prior to 1950. What is it? In the early 18th century discussions of ...
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179 views

Mathematical counterintelligence at Bletchley during World War 2

Popular works of fiction claim that after breaking the Enigma in Bletchley, some sophisticated mathematics or statistical techniques were used to hide this fact of breaking (not necessarily by the ...
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Why are the classic statistical approaches to NLP mostly generative models while the most recent ones are mostly discriminative?

Looking at the classic statistical approaches to natural language processing (e.g. tagging, parsing, etc.), I see that they are mostly generative models: n-gram models, Naive Bayes classifiers, hidden ...
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460 views

Was fake/rigged data common prior to the 20th century?

In one of the lab courses I took as an undergraduate, I remember that the professor noted while discussing some statistical test (almost certainly chi-squared) that one could use it to show that a lot ...