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Confidence Limits Program (CLP) calculates upper and lower confidence limits associated with observed outcome of N independent trials with M occurrences of event of interest. Calculates probability of event of interest for confidence levels of 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 96, 97, 98, and 99 percent. Provides graphical presentation of all limits and how they relate to maximum-likelihood value. Written in IBM PC BASIC.
Confidence limit is a routine requirement for Fourier spectral analysis. But this confidence limit is established based on ergodic theory: For stationary process, temporal average equals the ensemble average. Therefore, one can divide the data into n-sections and treat each section as independent realization. Most natural processes in general, and climate data in particular, are not stationary; therefore, there is a need for the Hilbert Spectral analysis for such processes. Here ergodic theory is no longer applicable. We propose to use various adjustable parameters in the shifting processes of the Empirical Mode Decomposition (EMD) method to obtain an ensemble of Intrinsic Mode Function 0 sets. Based on such an ensemble, we introduce a statistical measure in. a form of confidence limits for the Intrinsic Mode Functions, and consequently, the Hilbert spectra. The criterion of selecting the various adjustable parameters is based on the orthogonality test of the resulting M F sets. Length-of-day data from 1962 to 2001 will be used to illustrate this new approach. Its implication in climate data analysis will also be discussed.
Extension of exponential tolerance and confidence limits to class of distributions with monotone failure rate
Tolerance and confidence limits for classes of distributions based on failure rates
The utility of pivotal functions is established for assessing software reliability. Based on the Moranda geometric de-eutrophication model of reliability growth, confidence limits for attained reliability and prediction limits for the time to the next failure are derived using a pivotal function approach. Asymptotic approximations to the confidence and prediction limits are considered and are shown to be inadequate in cases where only a few bugs are found in the software. Departures from the assumed exponentially distributed interfailure times in the model are also investigated. The effect of these departures is discussed relative to restricting the use of the Moranda model.
Two different methods, classical and Bayesian, for determining confidence intervals involving Poisson-distributed data are compared. Particular consideration is given to cases where the number of counts observed is small and is comparable to the mean number of background counts. Reasons for preferring the Bayesian over the classical method are given. Tables of confidence limits calculated by the Bayesian method are provided for quick reference.
The calculation of limits for small numbers of astronomical counts is based on standard equations derived from Poisson and binomial statistics; although the equations are straightforward, their direct use is cumbersome and involves both table-interpolations and several mathematical operations. Convenient tables and approximate formulae are here presented for confidence limits which are based on such Poisson and binomial statistics. The limits in the tables are given for all confidence levels commonly used in astrophysics.
Technique developed for estimating reliability of software by use of Moranda geometric de-eutrophication model. Pivotal method enables straightforward construction of exact bounds with associated degree of statistical confidence about reliability of software. Confidence limits thus derived provide precise means of assessing quality of software. Limits take into account number of bugs found while testing and effects of sampling variation associated with random order of discovering bugs.
Estimating uncertainty in lifetime cancer risk for human exposure to space radiation is a unique challenge. Conventional risk assessment with low-linear-energy-transfer (LET)-based risk from Japanese atomic bomb survivor studies may be inappropriate for relativistic protons and nuclei in space due to track structure effects. This paper develops a Monte Carlo mixture model (MCMM) for transferring additive, National Institutes of Health multiplicative, and multiplicative excess cancer incidence risks based on Japanese atomic bomb survivor data to determine excess incidence risk for various US astronaut exposure profiles. The MCMM serves as an anchor point for future risk projection methods involving biophysical models of DNA damage from space radiation. Lifetime incidence risks of radiation-induced cancer for the MCMM based on low-LET Japanese data for nonleukemia (all cancers except leukemia) were 2.77 (90% confidence limit, 0.75-11.34) for males exposed to 1 Sv at age 45 and 2.20 (90% confidence limit, 0.59-10.12) for males exposed at age 55. For females, mixture model risks for nonleukemia exposed separately to 1 Sv at ages of 45 and 55 were 2.98 (90% confidence limit, 0.90-11.70) and 2.44 (90% confidence limit, 0.70-10.30), respectively. Risks for high-LET 200 MeV protons (LET=0.45 keV/micrometer), 1 MeV alpha-particles (LET=100 keV/micrometer), and 600 MeV iron particles (LET=180 keV/micrometer) were scored on a per particle basis by determining the particle fluence required for an average of one particle per cell nucleus of area 100 micrometer(2). Lifetime risk per proton was 2.68x10(-2)% (90% confidence limit, 0.79x10(-3)%-0. 514x10(-2)%). For alpha-particles, lifetime risk was 14.2% (90% confidence limit, 2.5%-31.2%). Conversely, lifetime risk per iron particle was 23.7% (90% confidence limit, 4.5%-53.0%). Uncertainty in the DDREF for high-LET particles may be less than that for low-LET radiation because typically there is very little dose-rate dependence. Probability density functions for high-LET radiation quality and dose-rate may be preferable to conventional risk assessment approaches. Nuclear reactions and track structure effects in tissue may not be properly estimated by existing data using in vitro models for estimating RBEs. The method used here is being extended to estimate uncertainty in spacecraft shielding effectiveness in various space radiation environments.
We conducted a historical cohort study of mortality among 195 astronauts who were exposed to space and medical sources of radiation between 1959 and 1991. Cumulative occupational and medical radiation exposures were obtained from the astronaut radiation exposure history data base. Causes of death were obtained from obligatory death certificates and autopsy reports that were on file in the medical records. A total of 18 deaths occurred during the 32-year follow-up period for which the all-cause standardized mortality ratio (SMR) was 142 (95 percent confidence interval 84 225). There was one cancer death in the buccal cavity and pharynegeal ICD-9 rubric whose occurrence was significantly beyond expectation. Mortality for coronary disease was 59 percent lower than expected (2 deaths; SMR = 41; 95 percent confidence limit 5 147). The crude death rate for 10 occupationally related accidents was 400 deaths per 100,000 person-years, which is an order of magnitude greater than accidental death rates in mining industries. The SMR of 1027 for fatal accidents was significantly beyond expectation (14 deaths; 95 percent confidence limit 561 1723) and was similar to SMRs for accidents among aerial pesticide applications. The 10-year cumulative risk of occupational fatalities based on the exponential, Weibull, Gompertz, and linear-exponential distributions was 10 percent. Mortality from motor vehicle accidents was slightly higher than expected but was not significant (1 death; SMR = 145; 95 percent confidence limit 2 808). Radiation exposures from medical procedures accounted for a majority of cumulative dose when compared with space radiation exposures. The results of the study do not confirm the impression that astronauts are at increased risk of cancer, but this does not obviate the need for further study. Overall, it was found that astronauts are at a health disadvantage as a result of catastrophic accidents.
Volume fraction of a constituent or phase was estimated in six specimens of conventional and DS-eutectic superalloys, using ASTM E562-76, a new standard recommended practice for determining volume fraction by systematic manual point count. Volume fractions determined ranged from 0.086 to 0.36, and with one exception, the 95 percent relative confidence limits were approximately 10 percent of the determined volume fractions. Since the confidence-limit goal of 10 percent, which had been arbitrarily chosen previously, was achieved in all but one case, this application of the new practice was considered successful.
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
The ortho/para ratio of H2O is shown to be an invariant in the cometary coma. The dependence of ortho-para ratio on temperature in thermal equilibrium is given, and the nuclear-spin-temperature is defined. Its relation to the physical temperature of the cometary ices is discussed, and the prospects for using the observed ortho/para ratio to infer properties of the cometary nucleus are explored. The ortho/para ratio in Halley's comet is derived from high resolution infrared spectra of near 2.7 microns wavelength. On UT December 24.1, 1985 it was 2.73 + or - 0.17, and on UT March 22.7, 1986 it was 3.23 + or - 0.37. The nuclear-spin-temperature was 35 K (+9 K, -5 K) pre-perihelion, and less than 40 K post-perihelion, at the 67% confidence limit. Both numbers are consistent with modeled values of the equilibrium temperature of the cometary nucleus at aphelion (47 K). However, at the 95% confidence limit they are also fully consistent with temperatures less than 50 K, corresponding to an ortho/para ratio of about 3.0.
Approach developed to establish utility of pivotal functions for estimation and prediction of reliability of software. Improved estimates of reliability with statistical confidence obtained when relatively few testing data available. Pivotal functions effective tools for determination of confidence limits for reliability of software and prediction limits for time to next failure. Provides exact confidence and prediction limits regardless of how many bugs found in software.
The calculation of the theoretical period of the Chandler wobble is extended to account for the non-hydrostatic portion of the earth's equatorial bulge and the effect of the fluid core upon the lengthening of the period due to the pole tide. The theoretical period of a realistic perfectly elastic earth with an equilibrium pole tide is found to be 426.7 sidereal days, which is 8.5 days shorter than the observed period of 435.2 days. Using Rayleigh's principle for a rotating earth, this discrepancy is exploited together with the observed Chandler Q to place constraints on the frequency dependence of mantle anelasticity. In all cases these limits arise from exceeding the 68 percent confidence limits of + or - 2.6 days in the observed period. Since slight departures from an equilibrium pole tide affect the Q much more strongly than the period, these limits are believed to be robust.
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. The degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.
A measurement, using the magnetic emulsion spectrometer system, of the differential rigidity spectrum of Z greater than or equal to 3 nuclei of the galactic cosmic radiation is presented. The system was flown on Aug. 22, 1969, from Palestine, Texas. The instrument floated above 125,000 feet for eight hours. The data in the rigidity range 8-285 GV can be represented by a power-law spectrum in rigidity, J(rho) = A rho to the minus gamma power, with the exponent gamma = 2.6 plus or minus 0.10. The spectrum in the range 15-285 GV is also described by the same exponent, gamma = 2.6 plus or minus 0.25. The data below 8 GV cannot be described by the same power law without invoking solar modulation. A set of nonunique parameters for modulation are given. Upper limit for the fraction of antimatter in the rigidity range 4-125 GV is .005 with 95% confidence limit.
We present an x-ray spectral study of 12 distant (z = 0.17-0.54) rich clusters of galaxies observed with the Einstein Observatory Imaging Proportional Counter. These x-ray spectral data show evidence for substantial excess absorptions beyond those expected in the galaxy, indicating the presence of large amounts of x-ray absorbing cool gas in these distant clusters. The mean value of the excess absorptions corresponds to an absorbing gas column density approximately greater than 10(exp 21)/sq cm. We calculate the x-ray luminosities of the clusters with observed fluxes only in the 0.8-3.5 keV band where the fluxes are less effected by the absorptions, and use the temperature-to-luminosity correlation (known only for nearby clusters) to estimate the temperatures of the hot intracluster medium (ICM) in the distant clusters. These temperature estimates, together with the spectral fits, provide further constraints on the column densities in the individual clusters. For the cluster CL 0016+16, the lower limit on the column density is found to be 8 x 10(exp 20)/sq cm at the 99 percent confidence limit. We also show that the ratio of the temperature obtained from the spectral fit to the temperature expected from the correlation tends to decrease with increasing look-back time, indicating possible temperature evolution of the hot ICM in the recent past. The inclusion of this evolutionary effect further increases the absorptions required in fitting the spectra.