Two-sided Prediction Interval Research Articles

Record ranked set sampling scheme

A new sampling scheme for generating record-breaking data is introduced and called record ranked set sampling (RRSS). A distribution-free two-sided prediction interval for future order statistics based on RRSS is derived. Numerical computations are obtained for comparing the results with the case based on ordinary records. Also, confidence intervals for quantiles of the parent distribution and prediction intervals for the ordinary records are given.

Practical use of the regression offset approach for the prediction of in vivo intrinsic clearance from hepatocytes

Systematic under-prediction of clearance is frequently associated with in vitro kinetic data when extrapolated using physiological scaling factors, appropriate binding parameters and the well-stirred model. The present study describes a method of removing this systematic bias through application of empirical correction factors derived from regression analyses applied to the in vitro and in vivo data for a defined set of reference compounds.Linear regression lines were established with in vivo intrinsic clearance (CLint), derived from in vivo clearance data and scaled in vitro intrinsic clearance from isolated hepatocyte incubations. The scaled CLint was empirically corrected to a predicted in vivo CLint using the slope and intercept from a uniform weighted linear regression applied to the in vitro to in vivo extrapolation.Cross validation of human data demonstrated that 66% of the reference compounds had a predicted in vivo CLint within two-fold of the observed value. The average absolute fold error (AAFE) for the in vivo CLint predictions was 1.90. For rat, 54% of the compounds had a predicted value within two-fold of the observed and the AAFE was 1.98.Three AstraZeneca projects are used to exemplify how a two-sided prediction interval, applied to the rat regression corrected reference data, can form the basis for assessing the likelihood that, for a given chemical series, the in vitro kinetic data is predictive of in vivo clearance and is therefore appropriate to guide optimisation of compound metabolic stability.

A note on the exact prediction limits for future observations from the inverse gaussian distribution

Through use of a result established by Tweedie (1957a), exact prediction interval for the mean of future observations can be derived straightforwardly. The conditions for which the exact prediction limits are two-sided are studied. The comparison of two-sided intervals among Padgett's approximation, Chhikara and Guttman frequentist approach and the exact inference developed here is made via extensive Monte Carlo simulations. In most simulation cases, the exact two-sided intervals (for the mean of future observations) obtained in this article are superior in terms of larger estimated coverage probabilities and shorter estimated average lengths. A summary and recommendation of the construction of two-sided prediction intervals for the mean of future observations from the inverse Gaussian distribution is included.

Factors for Calculating Prediction Intervals for Samples from a One-Parameter Exponential Distribution

Factors are provided for one-sided upper or lower, and two-sided prediction intervals for samples from a one-parameter exponential distribution. Some discussion regarding approximating these factors by f percentiles with non- integer numerator degrees o..

Two-Sided Prediction Intervals to Contain at Least k out of m Future Observations from a Normal Distribution

Prediction intervals are frequently used when it is necessary to use past data to make a statistical statement about a small number of future observations. Given the sample mean and the sample standard deviation s. computed from a random sample of size n from a normal distribution, this article provides factors r = r(k, m, n; γ) such that the two-sided prediction interval ± rs will contain at least k out of m future observations with (1ooγ)% confidence. The original n observations and the additional m observations are assumed to be independent samples from the same normal population. Values of r are given for γ = .90, .95, .99; n = 8(1)12, 1.5, 20, 25, 30, 40, 60, 120, 240, 480, X m = l(l)9 for k = m; m = 10, 15, 20(10)60, 80, 100, for k = m – j, where j = 0(l)8.

Two-Sided Prediction Intervals to Contain at LeastkOut ofmFuture Observations From a Normal Distribution

Two-Sided Prediction Intervals to Contain at Least<i>k</i>Out of<i>m</i>Future Observations From a Normal Distribution

Simultaneous Two-Sided Prediction Intervals to Contain at LeastlOut ofkFuture Means from a Normal Distribution

Given the sample mean and the sample standard deviation s computed from a random sample of size n from a N (μ, σ2) distribution, factors r = r(l, k, m, n; γ) are given such that the two-sided prediction interval ± rs will contain at least l out of k future means, computed from samples of size m, with (100γ)% confidence. The original n observations, and the additional k samples of m observations each, are assumed to be independent samples from the same normal population. Values of r are given for γ =0.90, 0.95, 0.99; n =8(1)12, 15, 20, 25, 30, 40, 60, 120, 240, 480, m =1, 5(5)20; k =1(1)9 and l = k; k = 10, 15, 20(10)60, 80, 100 and l = k − j, for j = 0,1.

Prediction Limits for the Inverse Gaussian Distribution

Prediction intervals for the inverse Gaussian are obtained from both a frequentist and a Bayesian viewpoint. The frequentist intervals are obtained by constructing pivotals that have the x 2 and F distributions. The method involves inversion of probability statements, which results in two-sided prediction intervals. A Bayesian predictive density is obtained using a vague prior, from which one- or two-sided Bayesian prediction intervals can be determined. An example for which Bayesian prediction limits are narrower than the frequentist is given.

Factors for Calculating Two-Sided Prediction Intervals for Samples from a Normal Distribution

Abstract Factors r(k, n; γ) for a normal distribution are given such that one may be 100γ% confident that the two-sided prediction interval will contain all of k future values, where and s are the sample mean and standard deviation from n previous observations. A special case is a prediction interval for a single future observation, which can also be obtained using percentage points of the Student t-distribution. Curves which indicate the extent to which two previously proposed approximations over-estimate r(k, n; γ) are also given. One of these, based on a Bonferroni Inequality, gives generally satisfactory results for all cases except for small n and large k, but frequently requires unusual percentage points of the Student t-distribution.

Factors for Calculating Two-Sided Prediction Intervals for Samples from a Normal Distribution

Abstract Factors r(k, n; γ) for a normal distribution are given such that one may be 100γ% confident that the two-sided prediction interval will contain all of k future values, where and s are the sample mean and standard deviation from n previous observations. A special case is a prediction interval for a single future observation, which can also be obtained using percentage points of the Student t-distribution. Curves which indicate the extent to which two previously proposed approximations over-estimate r(k, n; γ) are also given. One of these, based on a Bonferroni Inequality, gives generally satisfactory results for all cases except for small n and large k, but frequently requires unusual percentage points of the Student t-distribution.