The problem of deriving an upper tolerance limit for a ratio of two normally distributed random variables is addressed, when the random variables follow a bivariate normal distribution, or when they are independent normal. The derivation uses the fact that an upper tolerance limit for a random variable can be derived from a lower confidence limit for the cumulative distribution function (cdf) o...

Nomenclature AoA = Angle of Attack CDF = Cumulative Distribution Function CoG = Center of Gravity CoV = Coefficient of Variation DLR = Deutsches Zentrum fuer Luftund Raumfahrt (German Aerospace Center) hb = ratio of vehicle bottom height to vehicle height hb2 = height parameter, s. Appendix A H = height of vehicle KS = Kolmogorov-Smirnov distance L = length of vehicle L/Dmax = maximum lift-to-d...

The end-to-end performance of multibranch dual-hop wireless communication systems with nonregenerative relays and equal gain combiner (EGC) at the destination over independent Nakagami-m fading channels is studied. We present new closed form expressions for probability distribution function (PDF) and cumulative distribution function (CDF) of end-to-end signal to noise ratio (SNR) per branch in ...

An analytical expression of the cumulative distribution function (cdf) of the normalized signal-to-noise ratio SNR of the maximum ratio combiner (MRC) in correlated Rician fading channels has been derived. The expression is expressed as an infinite power series which can be computed very fast by truncation to a finite number of terms. The analytical expression can handle any number of receiving...

Submit Manuscript | http://medcraveonline.com Abbreviations: FFR: Fatigue Failure Rate; FFPN: Fleet of N Fatigue-Prone aircraft; AL: Airline; AC: Aircraft; SL: Safe Life; FS: Fail Safe; DT: Damage Tolerance; MIMAR: Modeling in Industrial Maintenance and Reliability; CDF: Cumulative Distribution Functions; RV: Random Variable; ML: Maximum Likelihood; MCh: Markov chain; CD: Crack Detection; FF: F...

The Laguerre method for the numerical inversion of Laplace transforms is a well known approach to the approximation of probability density functions (PDFs) and cumulative distribution functions (CDFs) of first passage times in Markov chains. Results are presented that relate the Laguerre generating functions and Laguerre coefficients of a PDF with those of the corresponding complementary CDF. T...

The flow velocity distribution in partially-filled circular pipe was investigated in this paper. The velocity profile is different from full-filled pipe flow, since the flow is driven by gravity, not by pressure. The research findings show that the position of maximum flow is below the water surface, and varies with the water depth. In the region of near tube wall, the fluid velocity is mainly ...

This paper presents a generalized approach to the performance analysis of relay-aided communication systems for 5G-and-beyond scenarios. A dual-hop decoding and forwarding scheme is considered in analysis. The relationship between outage cumulative distribution function (CDF) signal-to-noise ratio (SNR) exploited derive universal expression probability that valid all fading scenarios, irrespect...

Denote by X the set of actuarial risks, and let 0 ≤ X ∈ X be a random variable rv with cumulative distribution function cdf F x , decumulative distribution function ddf F x 1 − F x , and probability density function pdf f x . The functional H : X → 0,∞ is then referred to as a risk measure, and it is interpreted as the measure of risk inherent in X. Naturally, a quite significant number of risk...

In this letter, the performance of millimeter-wave (mmWave) communications with selection combining (SC) over non-identical fluctuating two-ray (FTR) fading channels is analyzed. Consequently, exact expressions and asymptotic approximations at high signal-to-noise ratio (SNR) regime moment generating function (MGF) probability density (PDF) maximum FTR variates are provided. To effect, mathemat...