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 parameter e is smaller than one, e is the eccentricity and a the semi-major axis of an ellipse.

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 an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If in any one calculation Ptolemy had had to invoke 83 epicycles all at once, while Copernicus never required more than one third this number, then ( in the sense obvious to Margenau ) Ptolemaic astronomy would be simpler than Copernican.

If an atom bomb in 1945 could destroy an entire city surely the atomic arsenal we now have is more than adequate to fulfill any military objective required of it.

If they feel that we are taking a long-term view of their problems and are prepared to enter into reasonably long-term association with them in their development activities, they will be much more likely to undertake the difficult tasks required.

If it is decided to make a small shift which may be required from military aid or special assistance funds, in order to carry out the purposes of the Mutual Security Act through this new peaceful program, this will be a hopeful sign to the world.

If you were required to file a declaration of estimated tax for the calendar year 1961, it is not necessary to pay the fourth installment otherwise due on January 15, 1962, if you file your income tax return Form 1040, and pay your tax in full for the calendar year 1961 by January 31, 1962.

If he had income other than wages subject to withholding, he may be required to file Form 1040.

If all forms of a paradigm are grouped together within the dictionary, a considerable reduction in the amount of information required is possible.

If the force required to remove the coatings is plotted against film thickness, a graph as illustrated schematically in Fig. 5 may characteristically result.

If, however, we are seeking the optimal R-stage policy for a given feed state, only one search for a maximum is required at the final step.

If all the operating variables were varied simultaneously, Af operations would be required to do the same job, and as R increases this increases very much more rapidly than the number of operations required by the dynamic program.

If high accuracy is required in preflight leveling, it is usually necessary to integrate or doubly integrate the accelerometer outputs ( this also minimizes the noise problem ).

If the drift error is systematic, it can be canceled with a bias circuit which can be arranged and adjusted to supply the required compensating current.

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

If a small heater is available for the coldest nights, a slab or basement cistern can inexpensively provide the required thermal mass.

If the assets used are not identical ( so a price divergence makes the trade temporarily lose money ), or the margin treatment is not identical, and the trader is accordingly required to post margin ( faces a margin call ), the trader may run out of capital ( if they run out of cash and cannot borrow more ) and go bankrupt even though the trades may be expected to ultimately make money.

If the character encoding for a web page is chosen appropriately then HTML character references are usually only required for a markup delimiting characters mentioned above, and for a few special characters ( or not at all if a native Unicode encoding like UTF-8 is used ).

If precise dates are required, the beginning may be set in 802 AD, when the founder of the Khmer Empire, Jayavarman II pronounced himself universal monarch ( chakravartin ) and declared independence from Java, and the end may be set in 1431 AD, when Thai invaders from the kingdom of Ayutthaya sacked Angkor and caused the Khmer elite to migrate to Phnom Penh.

If a demonstration of ability or knowledge is required by law before being allowed to perform a task or job, this is referred to as licensure.

If the medication is mixed with formulas containing iron or soya products, larger doses may be required, as these substances may alter the absorption of thyroid hormone from the gut.

If the team scores a touchdown, starting with the 2010 season, it is required to attempt a 2-point conversion.

If the liquid and vapor are not evenly distributed across the superficial tower area as it enters the packed bed, the liquid to vapor ratio will not be correct in the packed bed and the required separation will not be achieved.

If liberty is taken to mean " the ability to exercise one's rights as provided for by the law and nature " then this is true, but if it means " the state when one is not held to nor required to perform anything against their will " then this is clearly false.

If a significant amount of greens work is required in a film, then the Greens may be an identifiable sub-department, with its own team-often of a size numbering double figures-and hierarchy ( eg.