Tag: Statistics

Benford’s Law Revisited

Several researchers have observed that, in a wide variety of collections of numerical data, the leading --- or most significant --- decimal digits are not uniformly distributed, but conform to a logarithmic distribution. Of the nine possible values, $latex {D_1=1}&fg=000000$ occurs more than $latex {30\%}&fg=000000$ of the time while $latex {D_1=9}&fg=000000$ is found in less … Continue reading Benford’s Law Revisited →

The Improbability Principle and the Seanad Election

A by-election for the Seanad Éireann Dublin University constituency, arising from the election of Ivana Bacik to Dáil Éireann, is in progress. There are seventeen candidates, eight men and nine women. Examining the ballot paper, I immediately noticed an imbalance: the top three candidates, and seven of the top ten, are men. The last six … Continue reading The Improbability Principle and the Seanad Election →

How many numbers begin with a 1? More than 30%!

The irregular distribution of the first digits of numbers in data-bases provides a valuable tool for fraud detection. A remarkable rule that applies to many datasets was accidentally discovered by an American physicist, Frank Benford, who described his discovery in a 1938 paper, "The Law of Anomalous Numbers" [TM181 or search for “thatsmaths” at irishtimes.com]. … Continue reading How many numbers begin with a 1? More than 30%! →

Andrey Markov’s Brilliant Ideas are still a Driving Force

Imagine examining the first 20,000 letters of a book, counting frequencies and studying patterns. This is precisely what Andrey Markov did when he analyzed the text of Alexander Pushkin's verse novel Eugene Onegin. This work comprises almost 400 stanzas of iambic tetrameter and is a classic of Russian literature. Markov studied the way vowels and … Continue reading Andrey Markov’s Brilliant Ideas are still a Driving Force →

The Improbability Principle

Extremely improbable events are commonplace. “It's an unusual day if nothing unusual happens”. This aphorism encapsulates a characteristic pattern of events called the Improbability Principle. Popularised by statistician Sir David Hand, emeritus professor at Imperial College London, it codifies the paradoxical idea that extremely improbable events happen frequently.  [TM112 or search for “thatsmaths” at irishtimes.com]. We … Continue reading The Improbability Principle →

The Citizens’ Assembly: Why do 10 Counties have no Members?

Recently, the Irish Government established the Citizens' Assembly, a body of 99 citizens that will consider a number of constitutional issues. The Assembly meets on Saturday to continue its deliberations on the Eighth Amendment to the Constitution, which concerns the ban on abortion. It will report to the Oireachtas (Parliament) on this issue in June … Continue reading The Citizens’ Assembly: Why do 10 Counties have no Members? →

A Simple Growth Function

Three Styles of Growth Early models of population growth represented the number of people as an exponential function of time, $latex \displaystyle N(t) = N_0 \exp(t/\tau) &fg=000000$ where $latex {\tau}&fg=000000$ is the e-folding time. For every period of length $latex {\tau}&fg=000000$, the population increases by a factor $latex {e\approx 2.7}&fg=000000$. Exponential growth was assumed by … Continue reading A Simple Growth Function →