Search results for "exponential distribution"
showing 10 items of 21 documents
Large deviations results for subexponential tails, with applications to insurance risk
1996
AbstractConsider a random walk or Lévy process {St} and let τ(u) = inf {t⩾0 : St > u}, P(u)(·) = P(· | τ(u) < ∞). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time τ(u) is described as u → ∞. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for downwards skip-free processes like the classical compound Poisson insurance risk process where the formulation is in terms of total variation convergence. The ideas of the proof involve excursions and path decompositions for Mark…
Maximum probability estimators in the case of exponential distribution
1975
In 1966–1969L. Weiss andJ. Wolfowitz developed the theory of „maximum probability” estimators (m.p.e.'s). M.p.e.'s have the property of minimizing the limiting value of the risk (see (2.10).) In the present paper, therfore, after a short description of the new method, a fundamental loss function is introduced, for which—in the so-called regular case—the optimality property of the maximum probability estimators yields the classical result ofR.A. Fisher on the asymptotic efficiency of the maximum likelihood estimator. Thereby it turns out that the m.p.e.'s possess still another important optimality property for this loss function. For the latter the parameters of the exponential distribution—…
Comparing Performances of Turbo-roundabouts and Double-lane Roundabouts
2012
Starting from assumptions regarding the arrival process of circulating streams and according to models based on the gap-acceptance theory, the paper is aimed at comparing operational performances between basic turbo-roundabouts and double-lane roundabouts. The paper proposes applications of the Hagring model for entry capacity estimations at double-lane roundabouts and turbo-roundabouts, these latter, in particular, featured by movements with only one or two conflicting traffic streams. This model allows to use, in fact, a bunched exponential distribution to quantify the distribution of major vehicle headways; it also considers specific values different by each lane for behavioural paramete…
The Extinction of Generations in Generation-Dependent Bellman-Harris Branching Processes with Exponential Lifespan
1978
If V is the time when in a Bellman-Harris branching model the k-th generation disappears out of the population, and if all individuals have exponentially distributed lifespans, the asymptotic behavior of the tail of the distribution of the extinction time V , P(V > t), is obtained, even if the distributions of the lifespans and the offspring sizes vary generation-dependent. Furthermore the times of extinction of several successive generations can be specified for the generation- independent case of the Markov branching model in continuous time. If the initial number of individuals and the absolute time grow up appropriately linked, a Poisson limit theorem for generation sizes will be given.
On the fractional probabilistic Taylor's and mean value theorems
2016
In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main properties. Specifically, we show a characterization result by which the nth-order fractional equilibrium distribution is identical to the starting distribution if and only if it is exponential. The nth-order fractional equilibrium density is then used to prove a fractional probabilistic Taylor's theorem based on derivatives of Riemann-Liouville type. A fractional analogue of the probabilistic mean value theorem is thus developed for pairs of nonnegative rand…
Inclusion ratio based estimator for the mean length of the boolean line segment model with an application to nanocrystalline cellulose
2014
A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation…
Generating survival times to simulate Cox proportional hazards models
2005
Simulation studies present an important statistical tool to investigate the performance, properties and adequacy of statistical models in pre-specified situations. One of the most important statistical models in medical research is the proportional hazards model of Cox. In this paper, techniques to generate survival times for simulation studies regarding Cox proportional hazards models are presented. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived, which is useful in simulation studies. It is shown how the exponential, the Weibull and the Gompertz distribution can be applied to generate appropriate survival times f…
Local Reinforcement Effect of a Strain Gauge Installation on Low Modulus Materials
2005
The reinforcement effect of electrical resistance strain gauges is well documented in the technical literature. In this paper the local reinforcement effect in tension is studied by using a simple theoretical model by considering a strain gauge mounted on a semi-infinite plate having the same width of the strain gauge and subjected to a uniaxial tension load. Neglecting the effect of the adhesive layer and considering the interface shear stress as an exponential distribution, the proposed model gives a closed-form solution. In detail, this model permits a simple formula to be obtained which allows the user to correct the local reinforcement effect provided that a proper calibration is perfo…
The MLE of the mean of the exponential distribution based on grouped data is stochastically increasing
2016
Abstract This paper refers to the problem stated by Balakrishnan et al. (2002). They proved that maximum likelihood estimator (MLE) of the exponential mean obtained from grouped samples is stochastically ordered provided that the sequence of the successive distances between inspection times is decreasing. In this paper we show that the assumption of monotonicity of the sequence of distances can be dropped.
Finite-size-scaling study of the simple cubic three-state Potts glass: Possible lower critical dimension d=3.
1990
For small lattices with linear dimension L ranging from L=3 to L=8 we obtain the distribution function P(q) of the overlap q between two real replicas of the three-state Potts-glass model with symmetric nearest-neighbor interaction with a Gaussian distribution. A finite-size-scaling analysis suggests a zero-temperature transition to occur with an exponentially diverging correlation length ${\ensuremath{\xi}}_{\mathrm{SG}}$\ensuremath{\sim}exp(C/${\mathit{T}}^{\mathrm{\ensuremath{\sigma}}}$). This implies that d=3 is the lower critical dimension.