If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable

If is a wrapped Cauchy distribution with the parameter representing the parameters of the corresponding " unwrapped " Cauchy distribution in the variable y where, then

If the parameter is denoted θ then the estimator is typically written by adding a " hat " over the symbol:.

If the parameter is the bull's-eye of a target, and the arrows are estimates, then a relatively high variance means the arrows are dispersed, and a relatively low variance means the arrows are clustered.

If the parameter is the bull's-eye of a target, and the arrows are estimates, then a relatively high absolute value for the bias means the average position of the arrows is off-target, and a relatively low absolute bias means the average position of the arrows is on target.

* If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list ( sometimes called referential transparency ), i. e. if the pure function is again called with the same parameters, the same result will be returned ( this can enable caching optimizations such as memoization ).

If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered.

If we do not alter the system, then the parameter λ is unchanged from measurement to measurement ; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase.

If the parameter " dopefish " is added to the executable, a sample of burping is heard and Scott's Mystical Head is seen spinning in circles on the screen.

If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z < sub > 0 </ sub >.

( If the object represents a static field then the parameter is ignored and may be.

( If the object represents a static method then the first parameter is ignored and may be.

Based on Ginzburg – Landau theory, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a Taylor expansion in terms of the order parameter, P. If a sixth order expansion is used ( i. e. 8th order and higher terms truncated ), the free energy is given by:

If a probability distribution depends on a parameter, one may on the one hand consider — for a given value of the parameter — the probability ( density ) of the different outcomes, and on the other hand consider — for a given outcome — the probability ( density ) this outcome has occurred for different values of the parameter.

If the output is considered as undefined if a parameter is undefined then < tt > pow ( 1, qNaN )</ tt > should produce a qNaN.

If a Gaussian proposal density is used the variance parameter has to be tuned during the burn-in period.

If we use primes for derivatives with respect to parameter t, then

If the true value of the cosmological curvature parameter is larger than 10 < sup >− 3 </ sup > we will be able to distinguish between these three models even now.

If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function

If this rotation parameter were real, it would be possible for a 180 ° rotation to reverse the direction of time and of z.

* If then has a Bernoulli distribution with parameter.

If the appellate court does find a legal defect in the decision " below " ( i. e., in the lower court ), it may " modify " the ruling to correct the defect, or it may nullify (" reverse " or " vacate ") the whole decision or any part of it.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

If the resulting four kilobyte table size is too large for a given target platform, the table lookup operation can be performed with a single 256-entry 32-bit ( i. e. 1 kilobyte ) table by the use of circular rotates.

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

If a ) testimonies conflict one another, b ) there are a small number of witnesses, c ) the speaker has no integrity, d ) the speaker is overly hesitant or bold, or e ) the speaker is known to have motives for lying, then the epistemologist has reason to be skeptical of the speaker's claims.

If the object point be infinitely distant, all rays received by the first member of the system are parallel, and their intersections, after traversing the system, vary according to their perpendicular height of incidence, i. e. their distance from the axis.

If the above errors be eliminated, the two astigmatic surfaces united, and a sharp image obtained with a wide aperture — there remains the necessity to correct the curvature of the image surface, especially when the image is to be received upon a plane surface, e. g. in photography.

If, in an unsharp image, a patch of light corresponds to an object point, the center of gravity of the patch may be regarded as the image point, this being the point where the plane receiving the image, e. g., a focusing screen, intersects the ray passing through the middle of the stop.

If the ratio a '/ a be sufficiently constant, as is often the case, the above relation reduces to the condition of Airy, i. e. tan w '/ tan w = a constant.

If the creditworthiness of the issuer deteriorates ( e. g. rating downgrade ) and its credit spread widens, the bond price tends to move lower, but, in many cases, the call option part of the convertible bond moves higher ( since credit spread correlates with volatility ).

If the auction is passed out, i. e. no bids are made and only four passes are called, the hands are abandoned and the turn to deal passes in rotation.

If BCG is accidentally given to an immunocompromised patient ( e. g., an infant with SCID ), it can cause disseminated or life-threatening infection.

If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y ∈ A.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

If one eigenvalue is negative ( i. e., an imaginary frequency ), then the stationary point is a transition structure.

If both high priority substituents are on the same side of the double bond, i. e. in the cis configuration, then the stereoisomer is assigned a Z or Zusammen configuration.

If a 4, 5, 6, 8, 9, or 10 is thrown on the come-out roll ( i. e., if a point is set ), most casinos allow pass line bettors to take odds by placing from one to five times ( and at some casinos, up to 100 times ) the pass line bet behind the pass line.

If matrix support is polar ( e. g. paper, silica etc.

If two cofinal subsets of B have minimal cardinality ( i. e. their cardinality is the cofinality of B ), then they are order isomorphic to each other.

If the disk was not otherwise prepared with a custom format, ( e. g. for data disks ), 664 blocks would be free after formatting, giving 664 × 254 = 168, 656 bytes ( or almost 165 kB ) for user data.

* If is the norm ( usually noted as ) defined in the sequence space ℓ < sup >∞</ sup > of all bounded sequences ( which also matches the non-linear distance measured as the maximum of distances measured on projections into the base subspaces, without requiring the space to be isotropic or even just linear, but only continuous, such norm being definable on all Banach spaces ), and is lower triangular non-singular ( i. e., ) then

If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards ( i. e. the silver sides trail ).

If we assume the controller C, the plant P, and the sensor F are linear and time-invariant ( i. e., elements of their transfer function C ( s ), P ( s ), and F ( s ) do not depend on time ), the systems above can be analysed using the Laplace transform on the variables.

If, i. e., it has a large norm with each value of s, and if, then Y ( s ) is approximately equal to R ( s ) and the output closely tracks the reference input.