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cumulative distribution function

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Published: 01 January 2000
Fig. 4 Cumulative distribution function for the standard normal distribution More
Image
Published: 01 January 1997
Fig. 5 Cumulative distribution function for fatigue data from Table 1 based on assumed normal distribution More
Image
Published: 01 January 1997
Fig. 6 Cumulative distribution function for fatigue data from Table 1 based on an assumed log-normal distribution. More
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Published: 01 January 1997
Fig. 8 Approximate confidence limits on a cumulative distribution function showing uncertainty in the mean and standard deviation More
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009213
EISBN: 978-1-62708-176-4
... on the probability density function, cumulative distribution function, population mean and variance, and parameter and percentile estimation. binomial distribution cumulative distribution function exponential distribution log normal distribution normal distribution Poisson distribution population mean...
Image
Published: 30 August 2021
Fig. 9 Illustration of the discrete probability distribution method. CDF, cumulative distribution function More
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Published: 30 August 2021
Fig. 7 Illustration of sampling from a distribution using a random number generator. CDF, cumulative distribution function More
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Published: 30 August 2021
Fig. 8 Illustration of the Latin hypercube sampling method. CDF, cumulative distribution function More
Series: ASM Handbook
Volume: 24
Publisher: ASM International
Published: 15 June 2020
DOI: 10.31399/asm.hb.v24.a0006567
EISBN: 978-1-62708-290-7
... of the PSD results in a cumulative distribution function (CDF) representation of the distribution. As an example, Table 1 presents data for a mock PSD. Example data for both a count- and volume-based particle size distribution Table 1 Example data for both a count- and volume-based particle size...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002431
EISBN: 978-1-62708-194-8
..., is shown for this case in Fig. 4 . Fig. 4 Histogram of failure modes with their approximate discrete density function Cumulative Distribution Functions Plots of experimental data as density functions, as shown in Fig. 2 and 3 , provide some useful statistical information. Inferences...
Series: ASM Handbook
Volume: 13A
Publisher: ASM International
Published: 01 January 2003
DOI: 10.31399/asm.hb.v13a.a0003641
EISBN: 978-1-62708-182-5
... of experimental design and data analysis. A sample of test results of mass loss, mass gain, thickness loss, corrosion potential, corrosion rate, and pitting area may have a normal distribution. The following equations describe the normal probability distribution function, f ( x ), and the cumulative normal...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006803
EISBN: 978-1-62708-329-4
... to use 1 M + 1 as a weight instead of 1 M for the empirical distribution, to acknowledge the fact that the extrema (minimum and maximum) are not reached within a sample of value. The empirical (discrete) cumulative distribution function is then: (Eq 1) F ( x J ) = J...
Book Chapter

Series: ASM Desk Editions
Publisher: ASM International
Published: 01 December 1998
DOI: 10.31399/asm.hb.mhde2.a0003088
EISBN: 978-1-62708-199-3
...Abstract Abstract This article describes design factors for products used in engineering applications. The article groups these factors into three categories: functional requirements, analysis of total life cycle, and other major factors. These categories intersect and overlap, constituting...
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002369
EISBN: 978-1-62708-193-1
... of a histogram where the area under each segment of the curve represents the percentage of all cycle amplitudes within that range. The integral of the pdf is the cumulative distribution function (cdf), which starts at zero and goes to one with increasing amplitude. The complementary cdf, one minus the cdf...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... of a component during the intended service life is sought. To help answer these questions, define the probability density function (PDF), f X ( x ), and the cumulative distribution function (CDF), F X ( x ) (see Fig. 2 ). Areas under the PDF define the probabilities as shown. The CDF defines...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002476
EISBN: 978-1-62708-194-8
.... This second probability is given by the cumulative distribution function (CDF) for the resistance random variable ( F R ) evaluated at x , that is: (Eq 5) P 2 = F R ( x ) With the probability of failure defined as the product of these two probabilities, summed over all possible...
Series: ASM Handbook
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003382
EISBN: 978-1-62708-195-5
... for fatigue life. For comparison, shape parameter for commonly used metals is approximately 7.0, indicating a greater degree of scatter for composites. The same information can also be cast into another form, called a cumulative Weibull distribution function. This function is a cumulative sum of the density...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002432
EISBN: 978-1-62708-194-8
... ) = e − ∫ 0 t λ ( t ) d t = exp [ − ∫ 0 t λ ( t ) d t ] This function is independent of the specific failure distribution involved. The case of constant failure rate, that is, λ( t ) independent of time, has special interest: (Eq 6a) R ( t...
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0009212
EISBN: 978-1-62708-176-4
... of the random variable at which the cumulative distribution function, F ( x ), is 0.50. In other words, it is the value that divides the population into equal parts. For symmetrical distributions such as the normal distribution, the median and the mean are equal. For nonsymmetrical distributions...
Series: ASM Handbook
Volume: 17
Publisher: ASM International
Published: 01 August 2018
DOI: 10.31399/asm.hb.v17.a0006446
EISBN: 978-1-62708-190-0
... Acoustics Consider a longitudinal plane wave of particle displacement u ( x,t ) propagating in the x -direction in a nonlinear isotropic elastic solid. The ultrasonic wave is generated by a transmitter at x = 0, producing a time harmonic displacement function of t ; that is, u 0 ( t ) = U sin...