Truncating the exponential with a uniform distribution

For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution. Hence, the data is a truncated empirical process that we can approximate by a Poisson process when only a small portion of the sample is observed, as is the case for our applications. We derive the likelihood from standard arguments for point processes, acknowledging the size of the latent sample as the second parameter, and derive the maximum likelihood estimator for both. Consistency and asymptotic normality of the estimator for the Exponential parameter are derived from standard results on M-estimation. We compare the design with a simple random sample assumption for the observed durations. Theoretically, the derivative of the log-likelihood is less steep in the truncation-design for small parameter values, indicating a larger computational effort for root finding and a larger standard error. In applications from the social and economic sciences and in simulations, we indeed, find a moderately increased standard error when acknowledging truncation.

Correlation between Defects and Electrical Performances of Ion-Irradiated 4H-SiC p–n Junctions

In this study, 4H-SiC p–n junctions were irradiated with 700 keV He+ ions in the fluence range 1.0 × 1012 to 1.0 × 1015 ions/cm2. The effects of irradiation were investigated by current–voltage (I–V) and capacitance–voltage (C–V) measurements, while deep-level transient spectroscopy (DLTS) was used to study the traps introduced by irradiation defects. Modifications of the device’s electrical performances were observed after irradiation, and two fluence regimes were identified. In the low fluence range (≤1013 ions/cm2), I–V characteristics evidenced an increase in series resistance, which can be associated with the decrease in the dopant concentration, as also denoted by C–V measurements. In addition, the pre-exponential parameter of junction generation current increased with fluence due to the increase in point defect concentration. The main produced defect states were the Z1/2, RD1/2, and EH6/7 centers, whose concentrations increased with fluence. At high fluence (>1013 ions/cm2), I–V curves showed a strong decrease in the generation current, while DLTS evidenced a rearrangement of defects. The detailed electrical characterization of the p–n junction performed at different temperatures highlights the existence of conduction paths with peculiar electrical properties introduced by high fluence irradiation. The results suggest the formation of localized highly resistive regions (realized by agglomeration of point defects) in parallel with the main junction.

Exact Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censored Competing Risks Data

It is known that the lifetimes of items may not be recorded exactly. In addition, it is known that more than one risk factor (RisF) may be present at the same time. In this paper, we discuss exact likelihood inference for competing risk model (CoRiM) with generalized adaptive progressive hybrid censored exponential data. We derive the conditional moment generating function (ConMGF) of the maximum likelihood estimators of scale parameters of exponential distribution (ExpD) and the resulting lower confidence bound under generalized adaptive progressive hybrid censoring scheme (GeAdPHCS). From the example data, it can be seen that the PDF of MLE is almost symmetrical.

Perturbation Analysis of Rivlin-Ericksen Fluid on Heat Transfer in the Presence of Heat Absorption

The problem of visco-elastic Rivlin-Ericksen fluid flow past a semi- infinite vertical plate embedded in a porous medium with variable temperature and suction in the presence of a uniform transverse magnetic field and thermal buoyancy effect is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and some graphical results such as visco-elastic parameter Rm, heat absorption parameter Q, Grashof number Gr, Prandtl number Pr, time t, suction velocity parameter A, moving velocity parameter Up and an exponential parameter ε, for the velocity and temperature profiles within the boundary layer are presented. Skin-friction coefficient, Nusselt numbers are also discussed with the help of the tables.

Exact Likelihood Inference for an Exponential Parameter under Generalized Adaptive Progressive Hybrid Censoring

In this paper, we propose a new type censoring scheme named a generalized adaptive progressive hybrid censoring scheme (GenAdPrHyCS). In this new type censoring scheme, the experiment is assured to stop at a pre-assigned time. This censoring scheme is designed to correct the drawbacks in the AdPrHyCS. Furthermore, we discuss inference for one parameter exponential distribution (ExD) under GenAdPrHyCS. We derive the moment generating function of the maximum likelihood estimator (MLE) of scale parameter of ExD and the resulting lower confidence bound under GenAdPrHyCS.

Stochastic Inventory System With Different Rates of Production

This article analyzes a solitary item stochastic inventory model with two distinctive generation rates where a request pursues Poisson distribution and an item has a limited lifetime which is level dependent. It is expected that the framework be on a foreordained level and the framework is changed over to ON mode from OFF mode with a noteworthy exchanging time with exponential parameter α. During the switching time, no interest will be served, the interest during the exchange time is lost. Here, excesses are permitted and during accumulations, the production rate is higher than that of ordinary generation time. Some framework attributes are shown with time variety.

Technical note: An improved discharge sensitivity metric for young water fractions

Recent virtual and experimental investigations have shown that the young water fraction Fyw (i.e. the proportion of catchment outflow younger than circa 2–3 months) increases with discharge in most catchments. The discharge sensitivity of Fyw has been defined as the rate of increase in Fyw with increasing discharge (Q) and has been estimated by the linear regression slope between Fyw and Q, hereafter called DS(Q). The combined use of both metrics, Fyw and DS(Q), provides a promising method for catchment inter-comparison studies that seek to understand streamflow generation processes. Here we explore the discharge sensitivity of Fyw in the intensively sampled small Mediterranean research catchment Can Vila. Intensive sampling of high flows at Can Vila allows young water fractions to be estimated for the far upper tail of the flow frequency distribution. These young water fractions converge toward 1 at the highest flows, illustrating a conceptual limitation in the linear regression method for estimating DS(Q) as a metric of discharge sensitivity: Fyw cannot grow with discharge indefinitely, since the fraction of young water in discharge can never be larger than 1. Here we propose to quantify discharge sensitivity by the parameter of an exponential-type equation that expresses how Fyw varies with discharge. The exponential parameter (Sd) approximates DS(Q) at moderate discharges where Fyw is well below 1; however, the exponential equation and its discharge sensitivity metric better capture the non-linear relationship between Fyw and Q and are robust with respect to changes in the range of sampled discharges, allowing comparisons between catchments with strongly contrasting flow regimes.