In mathematics, an exponential function is a function of the form
Half-life is the time required for a quantity to reduce to half its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo, or how long stable atoms survive, radioactive decay. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.
In probability theory and statistics, the exponential distribution is the probability distribution that describes the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts.
Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function of time is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.
Exponential decay occurs in the same way when the growth rate is negative. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay, the function values forming a geometric progression. In either exponential growth or exponential decay, the ratio of the rate of change of the quantity to its current size remains constant over time.
In UNIX computing, the system load is a measure of the amount of computational work that a computer system performs. The load average represents the average system load over a period of time. It conventionally appears in the form of three numbers which represent the system load during the last one-, five-, and fifteen-minute periods.
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant:
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to differ by at most a constant factor.
The relative strength index (RSI) is a technical indicator used in the analysis of financial markets. It is intended to chart the current and historical strength or weakness of a stock or market based on the closing prices of a recent trading period. The indicator should not be confused with relative strength.
In statistics, a moving average is a calculation to analyze data points by creating a series of averages of different subsets of the full data set. It is also called a moving mean (MM) or rolling mean and is a type of finite impulse response filter. Variations include: simple, and cumulative, or weighted forms.
In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution, because it can be thought of as two exponential distributions spliced together back-to-back, although the term is also sometimes used to refer to the Gumbel distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution.
In futures studies and the history of technology, accelerating change is a perceived increase in the rate of technological change throughout history, which may suggest faster and more profound change in the future and may or may not be accompanied by equally profound social and cultural change.
Exponential smoothing is a rule of thumb technique for smoothing time series data using the exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign exponentially decreasing weights over time. It is an easily learned and easily applied procedure for making some determination based on prior assumptions by the user, such as seasonality. Exponential smoothing is often used for analysis of time-series data.
Trix is a technical analysis oscillator developed in the 1980s by Jack Hutson, editor of Technical Analysis of Stocks and Commodities magazine. It shows the slope of a triple-smoothed exponential moving average. The name Trix is from "triple exponential."
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on the idea of the function being proportional to the speed to which the function grows. The model is named after Thomas Robert Malthus, who wrote An Essay on the Principle of Population (1798), one of the earliest and most influential books on population.
The mass index is an indicator, developed by Donald Dorsey, used in technical analysis to predict trend reversals. It is based on the notion that there is a tendency for reversal when the price range widens, and therefore compares previous trading ranges.
The doubling time is the period of time required for a quantity to double in size or value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things that tend to grow over time. When the relative growth rate is constant, the quantity undergoes exponential growth and has a constant doubling time or period, which can be calculated directly from the growth rate.
In the statistics of time series, and in particular the analysis of financial time series for stock trading purposes, a moving-average crossover occurs when, on plotting two moving averages each based on different degrees of smoothing, the traces of these moving averages cross. It does not predict future direction but shows trends. This indicator uses two moving averages, a slower moving average and a faster moving average. The faster moving average is a short term moving average. For end-of-day stock markets, for example, it may be 5-, 10- or 25-day period while the slower moving average is medium or long term moving average. A short term moving average is faster because it only considers prices over short period of time and is thus more reactive to daily price changes. On the other hand, a long term moving average is deemed slower as it encapsulates prices over a longer period and is more lethargic. However, it tends to smooth out price noises which are often reflected in short term moving averages.
The true strength index (TSI) is a technical indicator used in the analysis of financial markets that attempts to show both trend direction and overbought/oversold conditions. It was first published William Blau in 1991.
The indicator uses moving averages of the underlying momentum of a financial instrument. Momentum is considered a leading indicator of price movements, and a moving average characteristically lags behind price. The TSI combines these characteristics to create an indication of price and direction more in sync with market turns than either momentum or moving average. The TSI is provided as part of the standard collection of indicators offered by various trading platforms.
In probability theory and directional statistics, a wrapped exponential distribution is a wrapped probability distribution that results from the "wrapping" of the exponential distribution around the unit circle.
