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Computer systems keep a log of users' access to the system. The term "log" comes from the chip log which was historically used to record distance traveled at sea and was recorded in a ship's log or logbook. To sign in connotes the same idea but is based on the analogy of manually signing a log book or visitor's book.
The log-t distribution has the probability density function: (, ^, ^) = (+) ^ (+ ( ^ ^)) +,where ^ is the location parameter of the underlying (non-standardized) Student's t-distribution, ^ is the scale parameter of the underlying (non-standardized) Student's t-distribution, and is the number of degrees of freedom of the underlying Student's t-distribution. [1]
The Student's t distribution plays a role in a number of widely used statistical analyses, including Student's t test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis.