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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
Method to find best fit of a time-series model
it if necessary), and using plots of the autocorrelation (ACF) and partial autocorrelation (PACF) functions of the dependent time series to decide which
Box–Jenkins_method
Correlation of a signal with a time-shifted copy of itself, as a function of shift
the autocorrelation of a real or complex random process is the Pearson correlation between values of the process at different times, as a function of the
Autocorrelation
Chart of correlation statistics
plotting.autocorrelation_plot R: functions acf and pacf Corrgrams: python seaborn: heatmap, pairplot R: corrgram Partial autocorrelation function Lag plot
Correlogram
Time series model
is designated as the maximum lag q. Sometimes the ACF and partial autocorrelation function (PACF) will suggest that an MA model would be a better model
Moving-average_model
Function returning one of only two values
Hamming weight of the function is the number of ones in the truth table. Bent: its derivatives are all balanced (the autocorrelation spectrum is zero) Correlation
Boolean_function
Statistical model used in time series analysis
using the sample autocorrelation function (ACF), partial autocorrelation function (PACF), and/or extended autocorrelation function (EACF) method. Other
Autoregressive integrated moving average
Autoregressive_integrated_moving_average
Function related to statistics and probability theory
L\equiv \left[{\frac {\partial L}{\partial \theta _{i}}}\right]_{i=1}^{n_{\mathrm {i} }}} vanishes, and if the likelihood function approaches a constant
Likelihood_function
Concept in probability theory and statistics
explain. In time series analysis, the partial autocorrelation function (sometimes "partial correlation function") of a time series is defined, for lag
Partial_correlation
Topics referred to by the same term
PACF may refer to: Partial autocorrelation function - a type of Mathematical Function. Princeton Area Community Foundation - a public charity based in
PACF
Statistical model used in time series analysis
found by plotting the partial autocorrelation functions. Similarly, q can be estimated by using the autocorrelation functions. Both p and q can be determined
Autoregressive moving-average model
Autoregressive_moving-average_model
Park test Partial autocorrelation – redirects to Partial autocorrelation function Partial autocorrelation function Partial correlation Partial least squares
List_of_statistics_articles
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
Mathematical transform that expresses a function of time as a function of frequency
instead take the Fourier transform of its autocorrelation function. The autocorrelation function R of a function f is defined by R f ( τ ) = lim T → ∞ 1
Fourier_transform
Power law growth of entropy of language or a stochastic process
_{k}^{2}=\infty } , where α k {\displaystyle \alpha _{k}} is the partial autocorrelation function. Additionally, if the Gaussian process has a positive and continuous
Hilberg's_hypothesis
Concept in probability and statistics
a function that gives the covariance of the process with itself at pairs of time points. Autocovariance is closely related to the autocorrelation of
Autocovariance
Statistical hypothesis test for the presence of serial correlation
Breusch and Leslie G. Godfrey. The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals
Breusch–Godfrey_test
Covariance and correlation
cross-correlation is similar in nature to the convolution of two functions. In an autocorrelation, which is the cross-correlation of a signal with itself, there
Cross-correlation
Test statistic
Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation at lag 1 in the residuals (prediction errors) from a regression analysis
Durbin–Watson_statistic
Statistical hypothesis test
desired false-rejection probability (e.g. 0.05). Since F is a monotone function of the likelihood ratio statistic, the F-test is a likelihood ratio test
F-test
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
Approximation method in statistics
, … , m , {\displaystyle {\frac {\partial S}{\partial \beta _{j}}}=2\sum _{i}r_{i}{\frac {\partial r_{i}}{\partial \beta _{j}}}=0,\ j=1,\ldots ,m,} and
Least_squares
Procedure to estimate standard deviation from a sample
the autocorrelation function (ACF) of the data. (Note that the expression in the brackets is simply one minus the average expected autocorrelation for
Unbiased estimation of standard deviation
Unbiased_estimation_of_standard_deviation
Measure of covariance of components of a random vector
{\displaystyle \operatorname {K} _{\mathbf {X} \mathbf {X} }} is related to the autocorrelation matrix R X X {\displaystyle \operatorname {R} _{\mathbf {X} \mathbf
Covariance_matrix
Representation of a type of random process
The autocorrelation function of an AR(p) process is a sum of decaying exponentials. Each real root contributes a component to the autocorrelation function
Autoregressive_model
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
to have unit variance, by standardizing the data and hence use the autocorrelation matrix instead of the autocovariance matrix as a basis for PCA. However
Principal_component_analysis
Calculation of complex statistical distributions
_{k=1}^{\infty }\rho _{k}} , is often called the integrated autocorrelation. When the chain has no autocorrelation ( ρ k = 0 {\displaystyle \rho _{k}=0} for all k
Markov_chain_Monte_Carlo
Special type of Boolean function
partially bent functions form a large class defined by a condition on the Walsh transform and autocorrelation functions. All affine and bent functions are partially
Bent_function
Statistical test
P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness
Ljung–Box_test
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
Probability of survival beyond any specified time
certain time. The survival function is also known as the survivor function or reliability function. The term reliability function is common in engineering
Survival_function
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
Medical imaging and optical technique
electric field temporal autocorrelation function is measured. A model for photon propagation through tissues, the measured autocorrelation signal is used to
Diffuse correlation spectrometry
Diffuse_correlation_spectrometry
Equation relating transport coefficients to correlation functions
{\displaystyle F_{e}=0} ) flux autocorrelation function is replaced by a thermostatted field dependent transient autocorrelation function. At time zero ⟨ J ( 0
Green–Kubo_relations
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
Sequence of data points over time
Consideration of the autocorrelation function and the spectral density function (also cross-correlation functions and cross-spectral density functions) Scaled cross-
Time_series
Type of deterministic method for multivariate interpolation
method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I). The name given to this type of method was
Inverse_distance_weighting
Type of stochastic process
K_{XX}(\tau )\triangleq K_{XX}(t_{1}-t_{2},0)} This also implies that the autocorrelation depends only on τ = t 1 − t 2 {\displaystyle \tau =t_{1}-t_{2}}
Stationary_process
Wigner distribution function in physics as opposed to in signal processing
probability distribution in phase space. It is a generating function for all spatial autocorrelation functions of a given quantum-mechanical wavefunction ψ(x). Thus
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting. A polynomial function is one that has
Polynomial and rational function modeling
Polynomial_and_rational_function_modeling
Family of probability distributions
{\displaystyle {\widehat {\sigma }}^{2}=\operatorname {E} (y_{i}^{2}),} and autocorrelation function r ( k ) = E ( y i , y i + k ) E ( y i 2 ) {\displaystyle r(k)={\frac
Tweedie_distribution
Method of estimating the parameters of a statistical model, given observations
{\partial \ell }{\partial \theta _{1}}}=0,\quad {\frac {\partial \ell }{\partial \theta _{2}}}=0,\quad \ldots ,\quad {\frac {\partial \ell }{\partial \theta
Maximum_likelihood_estimation
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
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
Statistical hypothesis test
portmanteau test in time-series analysis, testing for the presence of autocorrelation Likelihood-ratio tests in general statistical modelling, for testing
Chi-squared_test
Method used in statistics, pattern recognition, and other fields
linear combination that is the discriminant function. Like in a regression equation, these coefficients are partial (i.e., corrected for the other predictors)
Linear_discriminant_analysis
Perceptual property in music ordering sounds from low to high
their autocorrelation function do not elicit a corresponding pitch percept, and that certain sounds without a peak in their autocorrelation function nevertheless
Pitch_(music)
Circular statistical graph of proportionality
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Pie_chart
Function that measures dissimilarity between two probability distributions
_{p}^{j}}}{\tfrac {\partial }{\partial \theta _{q}^{k}}}D(p,q),\ \ \mathrm {etc.} \end{aligned}}} Now we restrict these functions to a diagonal p = q
Divergence_(statistics)
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
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
Table that displays the frequency of variables
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Contingency_table
Signal processing algorithm
)\,d\tau ,} where R s ( τ ) {\displaystyle R_{s}(\tau )} is the autocorrelation function of s ( t ) {\displaystyle s(t)} and R x s ( τ ) {\displaystyle
Wiener_filter
Function for integral Fourier-like transform
2013-08-10 at the Wayback Machine Rafiee, J.; Tse, Peter W. (2009). "Use of autocorrelation in wavelet coefficients for fault diagnosis". Mechanical Systems and
Wavelet
Bias in causal inference
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Confounding
Measure of linear correlation
{Y}}_{i})({\hat {Y}}_{i}-{\bar {Y}})=0} can be proved by noticing that the partial derivatives of the residual sum of squares (RSS) over β0 and β1 are equal
Pearson correlation coefficient
Pearson_correlation_coefficient
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)
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
Probabilistic problem-solving algorithm
McKean Jr. on Markov interpretations of a class of nonlinear parabolic partial differential equations arising in fluid mechanics. An earlier pioneering
Monte_Carlo_method
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
Non-parametric statistic used to estimate the survival function
estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the
Kaplan–Meier_estimator
Stochastic differential equation
correlation time of the noise term. It can also be shown that the autocorrelation function of the particle velocity v {\displaystyle \mathbf {v} } is given
Langevin_equation
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
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
Apparent lack of pattern or predictability in events
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Randomness
Integral expressing the amount of overlap of one function as it is shifted over another
derivative. More generally, in the case of functions of several variables, an analogous formula holds with the partial derivative: ∂ ∂ x i ( f ∗ g ) = ∂ f ∂
Convolution
Concept in inferential statistics
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Statistical_significance
Statistical property quantifying how much a collection of data is spread out
probability density function while leaving the mean (the expected value) unchanged. The concept of a mean-preserving spread provides a partial ordering of probability
Statistical_dispersion
Algorithm to estimate signal frequency
(average magnitude difference function), ASMDF (Average Squared Mean Difference Function), and other similar autocorrelation algorithms work this way. These
Pitch_detection_algorithm
Regression analysis
form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on
Nonlinear_regression
Statistical transformation
using standard normal theory and derivations. See also application to partial correlation. Hotelling gives a concise derivation of the Fisher transformation
Fisher_transformation
Measure of the deviation of position over time
denotes averaging over N ensembles. Also, one can easily derive the autocorrelation function from the MSD: ⟨ [ r ( t ) − r ( 0 ) ] 2 ⟩ = ⟨ r 2 ( t ) ⟩ + ⟨ r
Mean_squared_displacement
Sub-discipline of systems engineering that emphasizes dependability
equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended function adequately
Reliability_engineering
Range to estimate an unknown parameter
a Bayesian alternative for interval estimation Cumulative distribution function-based nonparametric confidence interval – Class of confidence intervals
Confidence_interval
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
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
Statistic measuring inter-rater agreement for categorical items
kappa: Nominal scale agreement with provision for scaled disagreement or partial credit". Psychological Bulletin. 70 (4): 213–220. doi:10.1037/h0026256
Cohen's_kappa
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
Interpretation of probability
of Iowa: 125 (fn. #52), 126. The works of Wald, Statistical Decision Functions (1950) and Savage, The Foundation of Statistics (1954) are commonly regarded
Bayesian_probability
Measure of the long-range dependence of a time series
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
Hurst_exponent
Statistical model to calculate the value of multiple quantities as they change over time
For multivariate tests for autocorrelation in the VAR models, see Hatemi-J, A. (2004). "Multivariate tests for autocorrelation in the stable and unstable
Vector_autoregression
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
Estimation procedure for correlated data
efficiency than generalized linear models (GLMs) in the presence of high autocorrelation. When the true working correlation is known, consistency does not require
Generalized estimating equation
Generalized_estimating_equation
Experiment in which information about the test is masked to reduce bias
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Blinded_experiment
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
Data visualization
can be useful to compare the box plot against the probability density function (theoretical histogram) for a normal N(0,σ2) distribution and observe their
Box_plot
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 quality control
Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey Time domain Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins)
Statistical_process_control
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
Standard score Information ratio Omega ratio Sampling (statistics) Variance function Everitt, Brian (1998). The Cambridge Dictionary of Statistics. Cambridge
Coefficient_of_variation
Smooth function in statistics
the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean. The variance function is a measure
Variance_function
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
Theory and technique of psychological measurement
"fit" than others. Today these differences, such as sensory and motor functioning (reaction time, visual acuity, and physical strength), are important
Psychometrics
Form of scientific experiment
(1901). "The influence of improvement in one mental function upon the efficiency of other functions (I)" (PDF). Psychological Review. 8 (3): 247. doi:10
Randomized_controlled_trial
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
Statistical distribution for dependence between random variables
1016/j.solener.2016.12.022. Munkhammar, J.; Widén, J. (2017). "An autocorrelation-based copula model for generating realistic clear-sky index time-series"
Copula_(statistics)
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
Class of statistical survival models
hazard function λ 0 ( t ) {\displaystyle \lambda _{0}(t)} over time. The partial likelihood can be maximized over β to produce maximum partial likelihood
Proportional_hazards_model
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
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
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
Boy/Male
Sikh
One on whom there is gods grace, Gods mercy
Boy/Male
Teutonic
Martial ruler.
Female
English
English Shakespeare character name derived from Roman Latin Porcius, PORTIA means "pig." A moon of Uranus was given this name.
Surname or Lastname
English
English : from Old French poutrel ‘colt’ (Late Latin pultrellus), a metonymic occupational name for someone responsible for keeping horses, or a nickname for a frisky and high-spirited person. This surname is also found in Ireland, Mac Lysaght believing it to be a variant of Purcell.
Boy/Male
Australian, Christian, French, Latin, Swiss
Warring; Like Mars; Roman God Mars
Girl/Female
Hindu, Indian
Queen
Male
German
Variant spelling of German Parzifal, PARSIFAL means "pierced valley."
Male
Spanish
Spanish form of Roman Latin Martialis, MARCIAL means "of/like Mars."
Male
German
German form of French Percevel, PARZIFAL means "pierced valley."
Male
English
English form of Roman Latin Martialis, MARTIAL means "of/like Mars."
Boy/Male
Latin
Warring.
Girl/Female
Hindu
Wisdom
Boy/Male
Muslim
Canvas
Boy/Male
Hindu
Lord of parti one of the name of Shri Satya Sai baba
Boy/Male
Hindu, Indian
Lord of Parti; One of the Name of Shri Satya Saibaba
Male
German
German form of French Percevel, PARZIVAL means "pierced valley."
Surname or Lastname
English
English : variant of Hartell.
Male
Irish
Irish Gaelic legend name, thought by some to have been derived from Latin Bartholomaeus, PARTHALÃN means "son of Talmai." As the legend goes, this name belonged to an early invader of Ireland who was the first to arrive on those shores after the biblical flood.
Girl/Female
Latin American Shakespearean
An offering. Portia was a heroine in Shakespeare's 'The Merchant of Venice'.
Male
Hungarian
Hungarian form of Greek Bartholomaios, BARTAL means "son of Talmai."
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
Girl/Female
English
Manly.
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, French, German, Latin, Swedish
Divine; Mythological Ancient Roman Divinity Diana was Noted for Beauty and Swiftness; Often Depicted as a Huntress
Boy/Male
Australian, British, English, Irish
From the Dales; The Valley Meadows
Girl/Female
Tamil
In flower, Bright as the dawn
Girl/Female
Hebrew, Hindu, Indian, Marathi
Goddess Parvati
Boy/Male
Muslim/Islamic
(related to Wahb)
Boy/Male
Hindu, Indian, Malayalam, Marathi
Lord of Speech
Female
English
Variant spelling of English Kayley, CAYLEY means "slender."
Girl/Female
Hebrew
Goat.
Boy/Male
Indian, Punjabi, Sikh
Insightful Light; King's Lamp
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
PARTIAL AUTOCORRELATION-FUNCTION
v.
Admitting of being parted; partible.
a.
Belonging to war, or to an army and navy; -- opposed to civil; as, martial law; a court-martial.
n.
A patrial noun. Thus Romanus, a Roman, and Troas, a woman of Troy, are patrial nouns, or patrials.
v. t.
To subject to trial by a court-martial.
a.
Not partial; not favoring one more than another; treating all alike; unprejudiced; unbiased; disinterested; equitable; fair; just.
n.
Inclined to favor one party in a cause, or one side of a question, more then the other; baised; not indifferent; as, a judge should not be partial.
a.
Impartial.
pl.
of Court-martial
a.
Of or pertaining to ancient Parthia, in Asia.
a.
Of, pertaining to, or suited for, war; military; as, martial music; a martial appearance.
a.
Both renal and portal. See Portal.
v.
Of or pertaining to a husband; as, marital rights, duties, authority.
n.
A native Parthia.
adv.
In part; not totally; as, partially true; the sun partially eclipsed.
a.
Pertaining to, or containing, iron; chalybeate; as, martial preparations.
n.
Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon.
a.
Serving as a partisan in a detached command; as, a partisan officer or corps.
n.
Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole.
adv.
In a partial manner; with undue bias of mind; with unjust favor or dislike; as, to judge partially.
v.
Given when departing; as, a parting shot; a parting salute.