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Probability of survival beyond any specified time
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time. The
Survival_function
Branch of statistics
Survival analysis is used in several ways: To describe the survival times of members of a group Life tables Kaplan–Meier curves Survival function Hazard
Survival_analysis
Distribution function associated with the empirical measure of a sample
an empirical distribution function (a.k.a. an empirical cumulative distribution function, eCDF) is the distribution function associated with the empirical
Empirical distribution function
Empirical_distribution_function
Non-parametric statistic used to estimate the survival function
limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure
Kaplan–Meier_estimator
Set of statistical processes for estimating the relationships among variables
regression models propose that Y i {\displaystyle Y_{i}} is a function (regression function) of X i {\displaystyle X_{i}} and β {\displaystyle \beta }
Regression_analysis
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Pearson correlation between values of the process at different times, as a function of the two times or of the time lag. Let { X t } {\displaystyle \left\{X_{t}\right\}}
Autocorrelation
Covariance and correlation
processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is also known as
Cross-correlation
Function of the observed sample results
for instance using Fisher's combined probability test. The p-value is a function of the chosen test statistic T {\displaystyle T} and is therefore a random
P-value
Class of statistical models
response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized
Generalized_linear_model
Conditional probability used in Bayesian statistics
| X ) {\displaystyle p(\theta |X)} . It contrasts with the likelihood function, which is the probability of the evidence given the parameters: p ( X |
Posterior_probability
Measure of covariance of components of a random vector
functions, the map shows statistical relations between different regions of the random functions. Statistically independent regions of the functions show
Covariance_matrix
Measure of variation in statistics
{erf} } is the error function. The proportion that is less than or equal to a number, x, is given by the cumulative distribution function: Proportion ≤ x =
Standard_deviation
Measure of the joint variability
{\displaystyle X} and Y {\displaystyle Y} have the following joint probability mass function, in which the six central cells give the discrete joint probabilities f
Covariance
Type of statistics
breakdown point and the influence function described below. The practical effect of problems seen in the influence function can be studied empirically by
Robust_statistics
Mathematical relation assigning a probability event to a cost
optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one
Loss_function
Function related to statistics and probability theory
A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability
Likelihood_function
Measure of linear correlation
cross-product of standardized variables Function of the angle between two standardized regression lines Function of the angle between two variable vectors
Pearson correlation coefficient
Pearson_correlation_coefficient
Statistical measure of association
the function cramerV() from the package rcompanion calculates V using the chisq.test function from the stats package. In contrast to the function cramersV()
Cramér's_V
Statistical measure of variability
reciprocal of the quantile function Φ − 1 {\displaystyle \Phi ^{-1}} (also known as the inverse of the cumulative distribution function) for the standard normal
Median_absolute_deviation
Statistic quantifying the association between two events
whether analyzing the OR as either disease survival or disease onset incidence – where the OR for survival is direct reciprocal of 1/OR for risk. This
Odds_ratio
The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents
List of probability distributions
List_of_probability_distributions
Measure of the asymmetry of random variables
} where Q is the quantile function (i.e., the inverse of the cumulative distribution function). The numerator is difference between the
Skewness
Statistical measure of how far values spread from their average
random variable X {\displaystyle X} is discrete with probability mass function x 1 ↦ p 1 , x 2 ↦ p 2 , … , x n ↦ p n {\displaystyle x_{1}\mapsto p_{1}
Variance
Graphical representation of the distribution of numerical data
and often for density estimation: estimating the probability density function of the underlying variable. The total area of a histogram used for probability
Histogram
Statistical test
that was found as the maximizing argument of the unconstrained likelihood function is compared with a hypothesized value θ 0 {\displaystyle \theta _{0}}
Wald_test
Estimator for quality of a statistical model
of fit (as assessed by the likelihood function), but it also includes a penalty that is an increasing function of the number of estimated parameters.
Akaike_information_criterion
Measure of the shape of a function
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
Middle quantile of a data set or probability distribution
point or an empty set). Every convex function is a C function, but the reverse does not hold. If f is a C function, then f ( med [ X ] ) ≤ med [ f
Median
Approximation method in statistics
describes the variance in a prediction of the dependent variable as a function of the independent variable and the deviations from the fitted curve. When
Least_squares
Nonparametric measure of rank correlation
relationship between two variables can be described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Function in actuarial science
function, usually written μ ( x ) {\displaystyle \mu (x)} , that gives the instantaneous rate at which deaths occur at age x, conditional on survival
Force_of_mortality
Statistical test comparing two probability distributions
distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two
Kolmogorov–Smirnov_test
Type of statistical measure over subsets of a dataset
viewed as a low-pass finite impulse response filter. Because the boxcar function outlines its filter coefficients, it is called a boxcar filter. It is sometimes
Moving_average
Fundamental theorem in probability theory and statistics
characteristic functions of a number of density functions becomes close to the characteristic function of the normal density as the number of density functions increases
Central_limit_theorem
Nonparametric test of the null hypothesis
WILCOXON function. KNIME implements the test in its Wilcoxon–Mann–Whitney Test node. ClickHouse implements the test in its mannWhitneyUTest function. The
Mann–Whitney_U_test
Statistical test that compares goodness of fit
}{\mathcal {L}}(\theta )\,\right]} is the logarithm of the maximized likelihood function L {\displaystyle {\mathcal {L}}} , and ℓ ( θ 0 ) {\displaystyle \ell (\theta
Likelihood-ratio_test
Statistical model used in time series analysis
augmented Dickey–Fuller test can assesses the stability of an intrinsic mode function and trend components. For stationary time series, the ARMA models can be
Autoregressive moving-average model
Autoregressive_moving-average_model
Study of collection and analysis of data
statistics. The term statistic, in singular form, is used to describe a function that returns its value of the same name. When census data cannot be collected
Statistics
Statistical hypothesis test
and so on. Let sgn {\displaystyle \operatorname {sgn} } denote the sign function: sgn ( x ) = 1 {\displaystyle \operatorname {sgn}(x)=1} if x > 0 {\displaystyle
Wilcoxon_signed-rank_test
Comparison of two distributions
distribution functions F and G, with associated quantile functions F−1 and G−1 (the inverse function of the CDF is the quantile function), the Q–Q plot
Q–Q_plot
Method used in statistics, pattern recognition, and other fields
discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method
Linear_discriminant_analysis
Diagnostic plot of binary classifier ability
The ROC can also be thought of as a plot of the statistical power as a function of the Type I Error of the decision rule (when the performance is calculated
Receiver operating characteristic
Receiver_operating_characteristic
Measure of statistical dispersion
calculated by integrating the probability density function (which yields the cumulative distribution function—any other means of calculating the CDF will also
Interquartile_range
Waiting time property of certain probability distributions
{\Pr(X>t+s)}{\Pr(X>s)}}=\Pr(X>t).} Rearranging the equality with the survival function, S ( t ) = Pr ( X > t ) {\displaystyle S(t)=\Pr(X>t)} , gives S (
Memorylessness
Probability distribution
instance of the hypergeometric function. For information on its inverse cumulative distribution function, see quantile function § Student's t-distribution
Student's_t-distribution
Numeric quantity representing the center of a collection of numbers
random variable and P ( x ) {\displaystyle P(x)} is the probability mass function. For a continuous distribution, the mean is ∫ − ∞ ∞ x f ( x ) d x {\displaystyle
Mean
Variable representing a random phenomenon
refers to neither randomness nor variability but instead is a mathematical function in which the domain is the set of possible outcomes in a sample space (e
Random_variable
Statistics concept
and leads to the concept of studentized residuals. Given an unobservable function that relates the independent variable to the dependent variable – say,
Errors_and_residuals
Numerical measure of a statistical relationship between variables
numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may be two columns of a given data
Correlation_coefficient
Generates a forecast of future values of a time series
exponential window function. Whereas in the simple moving average the past observations are weighted equally, exponential functions are used to assign
Exponential_smoothing
}\operatorname {coth} (t^{\beta }))}{\beta }}} The Hypertabastic survival function is defined as S ( t ) = sech [ α ( 1 − t β coth ( t β ) ) β ]
Hypertabastic_survival_models
Mathematical function for the probability a given outcome occurs in an experiment
often described by functions such as cumulative distribution functions, probability mass functions, or probability density functions. Which description
Probability_distribution
Linear regression model with a single explanatory variable
finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent
Simple_linear_regression
Process of using data analysis for predicting population data from sample data
on Survival Analysis applied to the Financial Industry. Archived from the original on Jan 16, 2026. Kruskal 1988 Freedman, D.A. (2008) "Survival analysis:
Statistical_inference
Statistic which divides a data set into 100 parts and analyzes it as a percentage
the percentile approximates the percentile function, the inverse of the cumulative distribution function. A related quantity is the percentile rank of
Percentile
Term in statistical hypothesis testing
exists using a given test in a given context. In typical use, it is a function of the specific test that is used (including the choice of test statistic
Power_(statistics)
Statistics applied to risk in insurance and other financial products
for example "commutation functions" (essentially precalculated columns of summations over time of discounted values of survival and death probabilities)
Actuarial_science
Probabilistic problem-solving algorithm
dimensions, but encounter two problems when the functions have many variables. First, the number of function evaluations needed increases rapidly with the
Monte_Carlo_method
Statistic for rank correlation
distribution of Y conditional to X has zero variance so that a bijective function f with f(X)=Y exists. The Stuart-Kendall Tau-c coefficient is defined as:
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Type of average of a collection of numbers
especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. If a numerical property, and
Arithmetic_mean
Method of statistical inference
consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference
Bayesian_inference
Statistical hypothesis test for forecasting
intensity function is used to represent the probability of a neuron spiking, conditioned on its own history. The conditional intensity function expresses
Granger_causality
Inverse of the average of the inverses of a set of numbers
x_{n})={\tfrac {1}{n}}\sum _{i=1}^{n}x_{i}.} The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive
Harmonic_mean
Non-parametric method for testing whether samples originate from the same distribution
airquality, and the analysis is included in the documentation for the R function kruskal.test. Boxplots of ozone values by month are shown in the figure
Kruskal–Wallis_test
Statistical method
choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed
Bootstrapping_(statistics)
Value that appears most often in a set of data
random variable, the mode is the value x at which the probability mass function P(X) takes its maximum value, i.e., x = argmaxxi P(X = xi). In other words
Mode_(statistics)
Partial correlation of a time series with its lagged values
In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values
Partial autocorrelation function
Partial_autocorrelation_function
Statistical relationship
variables (which in turn may be present even when one variable is a nonlinear function of the other). Other correlation coefficients, such as Spearman's rank
Correlation
Statistical considerations on how many observations to make
simulation, by Mead's resource equation, or by the cumulative distribution function: The table shown on the right can be used in a two-sample t-test to estimate
Sample_size_determination
Statistical modeling method
of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile
Linear_regression
Statistical model validation technique
vector xi are denoted xi1, ..., xip. If least squares is used to fit a function in the form of a hyperplane ŷ = a + βTx to the data (xi, yi) 1 ≤ i ≤ n
Cross-validation_(statistics)
Frequency with which an engineered system or component fails
number of systems. For convenience we first define the reliability (or survival function) as: R ( t ) = 1 − F ( t ) = Pr ( T > t ) {\displaystyle R(t)=1-F(t)=\Pr(T>t)}
Failure_rate
Statistical distribution for dependence between random variables
theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each variable is uniform
Copula_(statistics)
Metric for fit of statistical models
(}F(Y_{u})\,-\,F(Y_{l}){\bigg )}\,N} where: F = the cumulative distribution function for the probability distribution being tested. Yu = the upper limit for
Goodness_of_fit
Overview of and topical guide to statistics
Outlier Statistical graphics Histogram Frequency distribution Quantile Survival function Failure rate Scatter plot Bar chart Design of experiments Optimal
Outline_of_statistics
Sequence of data points over time
the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions) Scaled cross- and
Time_series
Statistical model for a binary dependent variable
the value "1"), hence the labeling; the function that converts log-odds to probability is the logistic function, hence the name. The unit of measurement
Logistic_regression
Statistical model for count data
models with the logarithm as the (canonical) link function, and the Poisson distribution function as the assumed probability distribution of the response
Poisson_regression
Statistical test used on paired nominal data
is the binomial distribution probability mass function and n = b + c. Binomial distribution functions are readily available in common software packages
McNemar's_test
Statistical property quantifying how much a collection of data is spread out
formed by spreading out one or more portions of A's probability density function while leaving the mean (the expected value) unchanged. The concept of a
Statistical_dispersion
Statistical matching technique
same as radius matching, except control observations are weighted as a function of the distance between the treatment observation's propensity score and
Propensity_score_matching
Method of estimating the parameters of a statistical model
\theta } . Then the function: θ ↦ f ( x ∣ θ ) {\displaystyle \theta \mapsto f(x\mid \theta )\!} is known as the likelihood function and the estimate: θ
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Processes that maintain quality at a constant level
hence around 1840 tolerance limits were introduced, wherein a design would function if its parts were measured to be within the limits. Quality was thus precisely
Quality_control
Method of data analysis
either via the pca command or via the princomp() function. Julia – Supports PCA with the pca function in the MultivariateStats package. KNIME – A java
Principal_component_analysis
Parametric model in survival analysis
censored observations one needs the survival function, which is the complement of the cumulative distribution function, i.e. one needs to be able to evaluate
Accelerated failure time model
Accelerated_failure_time_model
Concept; act of surviving
Survival or survivorship, the act of surviving, is the propensity of something to continue existing despite conditions that might kill or destroy it. The
Survival
Statistical value representing the center or average of a distribution
correspondence is: The associated functions are called p-norms: respectively 0-"norm", 1-norm, 2-norm, and ∞-norm. The function corresponding to the L0 space
Central_tendency
Model for generating observable data in probability and statistics
{\displaystyle P(Y\mid X)} can also be interpreted as a (non-deterministic) target function f : X → Y {\displaystyle f\colon X\to Y} , considering X as inputs and
Generative_model
Criterion for model selection
lower BIC are generally preferred. It is based, in part, on the likelihood function and it is closely related to the Akaike information criterion (AIC). When
Bayesian information criterion
Bayesian_information_criterion
Class of statistical survival models
accelerated (or decelerated). Survival models can be viewed as consisting of two parts: the underlying baseline hazard function, often denoted λ 0 ( t ) {\displaystyle
Proportional_hazards_model
Relationship between items in a set
the free dictionary. RANKNUM, a Matlab function to compute the five types of ranks Matlab Toolbox with functions to compute ranks TrueSkill Ranking System
Ranking
Generalization of the one-dimensional normal distribution to higher dimensions
scalar-valued function of a normal vector, its probability density function, cumulative distribution function, and inverse cumulative distribution function can
Multivariate normal distribution
Multivariate_normal_distribution
Functional relationship between two quantities
(mass) function directly, these methods introduce an implicit bias in the representation of the data, and thus should be avoided. The survival function, on
Power_law
N-th root of the product of n numbers
and then returning the result to linear scale by using the exponential function exp {\displaystyle \exp } , a 1 a 2 ⋯ a n t n = exp ( ln a 1 + ln
Geometric_mean
Probability distribution
{\displaystyle \phi (x)} denote the standard normal probability density function ϕ ( x ) = 1 2 π e − x 2 2 {\displaystyle \phi (x)={\frac {1}{\sqrt {2\pi
Skew_normal_distribution
t-test stem-and-leaf display stratified sampling survey methodology survival function survivorship bias symmetric probability distribution systematic sampling
Glossary of probability and statistics
Glossary_of_probability_and_statistics
Compilation of information about a given population
surveys. Although population and citizenship estimates remain an important function of a census, including exactly the geographic distribution of the population
Census
Time series model
that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms; often the
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Type of mathematical function
product of other distributions. If a density is log-concave, so is its survival function. If a density is log-concave, it has a monotone hazard rate (MHR)
Logarithmically concave function
Logarithmically_concave_function
Type of stochastic process
F_{X}(x_{t_{1}+\tau },\ldots ,x_{t_{n}+\tau })} represent the cumulative distribution function of the unconditional (i.e., with no reference to any particular starting
Stationary_process
SURVIVAL FUNCTION
SURVIVAL FUNCTION
Boy/Male
Muslim
Servant of the survivor
Girl/Female
Tamil
Happiness, Survivor
Surname or Lastname
English
English : variant of Sidlock, from a Middle English survival of an Old English personal name, SidlÄc.Americanized form of Czech Sedlak.
Boy/Male
English
Biblical Shadrach; one of three young Hebrew men who survived being cast into a fiery furnace.
Male
Greek
(Ζώσιμος) Greek name derived from the word zosimos, ZOSIMOS means "likely to survive; survivor."
Girl/Female
Tamil
Happiness, Survivor
Boy/Male
Afghan, Arabic, French, Hindu, Indian, Muslim, Sindhi
Saved; Rescued; Close Friend; Survivor; Safe
Girl/Female
Australian, Farsi, Gothic, Hindu, Indian, Iranian
Survivor
Male
Spanish
Spanish form of Latin Zosimus, SOSIMO means "likely to survive; survivor."
Boy/Male
English
Biblical Shadrach; one of three young Hebrew men who survived being cast into a fiery furnace.
Boy/Male
Indian
Survival, Immortality
Boy/Male
Arabic, Muslim
Survival; Immortality; Eternity
Boy/Male
Muslim
Survival, Immortality
Girl/Female
Hindu
Happiness, Survivor
Surname or Lastname
English
English : patronymic from an unidentified medieval personal name, perhaps a survival of Old English HÌ„nci or HÌ„nca. Compare Hinckley.
Female
Greek
(Ζώσιμη) Feminine form of Greek Zosimos, ZOSIME means "likely to survive; survivor."
Girl/Female
Hindu
Happiness, Survivor
Girl/Female
Muslim
Happiness, Survivor
Boy/Male
Arabic, Muslim
Servant of the Survivor
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Pure
SURVIVAL FUNCTION
SURVIVAL FUNCTION
Girl/Female
Hindu, Indian, Kannada, Marathi
A Name of a Sage; A Star
Boy/Male
Tamil
Earth, Universe
Male
African
master.
Boy/Male
Hindu, Indian
Great
Girl/Female
Indian, Malayalam, Tamil
Flower Archid; A Star
Girl/Female
Gaelic
Girl; lass.
Boy/Male
Tamil
Ramcharan | ராமசரணÂ
Feet of Ram
Boy/Male
Tamil
A legendary gem, A gem worn by Lord Vishnu
Girl/Female
Muslim
Gem, Jewel
Surname or Lastname
English
English : habitational name from any of various places, for example in Oxfordshire (formerly in Berkshire) and Lancashire, so named from Old English lang, long ‘long’ + worð ‘enclosure’.
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
n.
Any habit, usage, or belief, remaining from ancient times, the origin of which is often unknown, or imperfectly known.
a.
Surgical
v. t.
To live beyond the life or existence of; to live longer than; to outlive; to outlast; as, to survive a person or an event.
n.
Surmise.
n.
The state of being a survivor.
n.
A survivor.
v. t.
A kind of blunt-pointed surgical instrument.
v. t.
To survive; to outlive.
imp. & p. p.
of Survive
p. pr. & vb. n.
of Survive
n.
One who survives or outlives another person, or any time, event, or thing.
v. i.
To remain alive; to continue to live.
n.
One who survives; a survivor.
v. t.
To become, or survive as, the widow of.
n.
The longer liver of two joint tenants, or two persons having a joint interest in anything.
a.
Of or pertaining to surgeons or surgery; done by means of surgery; used in surgery; as, a surgical operation; surgical instruments.
n.
A living or continuing longer than, or beyond the existence of, another person, thing, or event; an outliving.
n.
Survey.
n.
See Murnival.
n.
In the game of gleek, four cards of the same value, as four aces or four kings; hence, four of anything.