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Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time ...
Exponential smoothing. Exponential smoothing or exponential moving average (EMA) 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.
A moving average is commonly used with time series data to smooth out short-term fluctuations and highlight longer-term trends or cycles. The threshold between short-term and long-term depends on the application, and the parameters of the moving average will be set accordingly. It is also used in economics to examine gross domestic product ...
Linear trend estimation. Linear trend estimation is a statistical technique used to analyze data patterns. When a series of measurements of a process are treated as a sequence or time series, trend estimation can be used to make and justify statements about tendencies in the data by relating the measurements to the times at which they occurred.
Failure rate is the frequency with which an engineered system or component fails, expressed in failures per unit of time. It is usually denoted by the Greek letter λ (lambda) and is often used in reliability engineering . The failure rate of a system usually depends on time, with the rate varying over the life cycle of the system.
Trend-stationary process. In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. [1] The trend does not have to be linear.
The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases. Studies involving the Hurst exponent were originally developed in hydrology for the practical matter of determining optimum dam ...
Population growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. [2] The global population has grown from 1 billion in 1800 to 7.9 billion in 2020. [3] The UN projected population to keep growing, and estimates have put ...