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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
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
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
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
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
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
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
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
Empirical law on the variance of species in a habitat
gene structures in number theory with sequential values of the Mertens function and also with the distribution of prime numbers from the eigenvalue deviations
Taylor's_law
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
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
Measure of distance between two proportions
In R, Cohen's h can be calculated using the ES.h function in the pwr package or the cohenH function in the rcompanion package. Cohen provides the following
Cohen's_h
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
Number taken as representative of a list of numbers
relevant (such as where a histogram, bar chart, or probability density function is being referenced), or to find a value that represents the majority of
Average
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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. It is greater than or equal to the minimum of its arguments: for positive
Harmonic_mean
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
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
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 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
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
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)
Probability that random variable X is less than or equal to x
{P} (T>t)=1-F_{T}(t).} In survival analysis, F ¯ X ( x ) {\displaystyle {\bar {F}}_{X}(x)} is called the survival function and denoted S ( x ) {\displaystyle
Cumulative distribution function
Cumulative_distribution_function
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
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
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
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
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
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 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 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
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)
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
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
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
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
Mathematical equation related to human death rate
for all ages, then the associated survival function S ( x ) {\displaystyle S(x)} and cumulative distribution function F ( x ) {\displaystyle F(x)} define
Gompertz–Makeham law of mortality
Gompertz–Makeham_law_of_mortality
Statistics concept
statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the
Polynomial_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)
}\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
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
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
Statistical sampling technique
only one in each axis-aligned hyperplane containing it. When sampling a function of N {\displaystyle N} variables, the range of each variable is divided
Latin_hypercube_sampling
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
Statistical theorem
{E} [L(\delta (X))]} where the "loss function" L {\displaystyle L} may be any convex function. If the loss function is twice-differentiable, as in the case
Rao–Blackwell_theorem
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
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
Type of numerical analysis
form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing. Another application is nonmetric multidimensional
Isotonic_regression
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
Statistical transformation
(r),} where "ln" is the natural logarithm function and "artanh" is the inverse hyperbolic tangent function. If (X, Y) has a bivariate normal distribution
Fisher_transformation
Statistical property
as GLS can exhibit strong bias in small samples if the actual skedastic function is unknown. Because heteroscedasticity concerns expectations of the second
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistical measure to determine how suited data is for factor analysis
and p j k {\displaystyle p_{jk}} is the partial correlation. This is a function of the squared elements of the `image' matrix compared to the squares of
Kaiser–Meyer–Olkin_test
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
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
Signal representation
statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than
Frequency_domain
SURVIVAL FUNCTION
SURVIVAL FUNCTION
Boy/Male
Afghan, Arabic, French, Hindu, Indian, Muslim, Sindhi
Saved; Rescued; Close Friend; Survivor; Safe
Boy/Male
Muslim
Survival, Immortality
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Pure
Boy/Male
English
Biblical Shadrach; one of three young Hebrew men who survived being cast into a fiery furnace.
Boy/Male
Arabic, Muslim
Survival; Immortality; Eternity
Girl/Female
Australian, Farsi, Gothic, Hindu, Indian, Iranian
Survivor
Girl/Female
Muslim
Happiness, 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.
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.
Girl/Female
Tamil
Happiness, Survivor
Girl/Female
Hindu
Happiness, Survivor
Boy/Male
Indian
Survival, Immortality
Female
Greek
(Ζώσιμη) Feminine form of Greek Zosimos, ZOSIME means "likely to survive; survivor."
Male
Greek
(Ζώσιμος) Greek name derived from the word zosimos, ZOSIMOS means "likely to survive; survivor."
Girl/Female
Tamil
Happiness, Survivor
Boy/Male
Arabic, Muslim
Servant of the 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.
Girl/Female
Hindu
Happiness, Survivor
Boy/Male
Muslim
Servant of the survivor
SURVIVAL FUNCTION
SURVIVAL FUNCTION
Boy/Male
Hindu
Lord of the form
Surname or Lastname
English
English : habitational name from Newbrough in Northumberland, named from Old English nīwe ‘new’ + burh ‘fortification’.English : In some instances, possibly a variant of Newberry.
Boy/Male
Muslim
Glow of the religion (Islam)
Girl/Female
Bengali, Indian
Creative Woman; Prayers for Others; Who Won Beauty
Girl/Female
Australian, Swedish
God has Favored Me
Boy/Male
American, Anglo, Australian, British, English
From the Hare's Hill; Meadow of the Hares
Boy/Male
Egyptian
He who brings back the distant one.
Boy/Male
Hindu, Indian, Marathi
Handsome
Girl/Female
Hindu, Indian, Marathi
King of Diamond; Gem of Serpents
Girl/Female
Tamil
Goddess Lakshmi, Auspicious, Luster, Prosperity, Pratham, Shrestha
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
SURVIVAL FUNCTION
v. t.
A kind of blunt-pointed surgical instrument.
a.
Of or pertaining to surgeons or surgery; done by means of surgery; used in surgery; as, a surgical operation; surgical instruments.
n.
In the game of gleek, four cards of the same value, as four aces or four kings; hence, four of anything.
n.
The longer liver of two joint tenants, or two persons having a joint interest in anything.
n.
Surmise.
n.
Survey.
v. t.
To become, or survive as, the widow of.
imp. & p. p.
of Survive
n.
Any habit, usage, or belief, remaining from ancient times, the origin of which is often unknown, or imperfectly known.
p. pr. & vb. n.
of Survive
n.
One who survives or outlives another person, or any time, event, or thing.
n.
A living or continuing longer than, or beyond the existence of, another person, thing, or event; an outliving.
v. i.
To remain alive; to continue to live.
n.
A survivor.
n.
See Murnival.
n.
The state of being a survivor.
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.
v. t.
To survive; to outlive.
n.
One who survives; a survivor.
a.
Surgical