Changes In Kurtosis Research Articles

General statistics of geographically dispersed wind power

AbstractThe paper examines the variability of wind power generated by wind farms that are geographically dispersed in a region. The reduced variability of wind power generation with increasing region size and number of wind farms is referred to as the smoothing effect. In this paper, the smoothing effect is quantified by changes in standard deviation, skewness and kurtosis of hourly wind power generation and its temporal gradients. General approximative equations are derived that allow the calculation of these parameters in dependence of the region size and the mean generation. It is shown from which point on the smoothing effect depends only on the region size and no longer on the number of wind farms. Upscaling can then be an appropriate method to simulate future wind power generation as smoothing effects are no longer neglected. This paper also shows how approximative duration curves of wind power generation or its temporal gradients can be simulated by means of the calculated parameters. Hence, the analysis can be used to assess unmeasured or potential wind power generation i n a region. The presented approach and equations are verified by German and Irish generation data. Copyright © 2010 John Wiley & Sons, Ltd.

An integrative model of motor unit activity during sustained submaximal contractions

The purpose of the study was to expand a model of motor unit recruitment and rate coding (30) to simulate the adjustments that occur during a fatiguing contraction. The major new components of the model were the introduction of time-varying parameters for motor unit twitch force, recruitment, discharge rate, and discharge variability, and a control algorithm that estimates the net excitation needed by the motoneuron pool to maintain a prescribed target force. The fatigue-induced changes in motor unit activity in the expanded model are a function of changes in the metabolite concentrations that were computed with a compartment model of the intra- and extracellular spaces. The model was validated by comparing the simulation results with data available from the literature and experimentally recorded in the present study during isometric contractions of the first dorsal interosseus muscle. The output of the model was able to replicate a number of experimental findings, including the time to task failure for a range of target forces, the changes in motor unit discharge rates, the skewness and kurtosis of the interspike interval distributions, discharge variability, and the discharge characteristics of newly recruited motor units. The model output provides an integrative perspective of the adjustments during fatiguing contractions that are difficult to measure experimentally.

Experimental and forecasted values of the ultraviolet index in southwestern Spain

The ultraviolet (UV) index is a standard vehicle for informing the public about the magnitude of the UV radiation reaching the Earth's surface and its potential harmful effects over the human health. The first objective of this article is to analyze experimental values of the UV index in three stations located in southwestern Spain during five years (2001–2005). The study reports reliable fundamental statistical parameters, which can serve as relevant values for comparison with other regions and model results. The results show a great influence of the astronomical factors in the seasonal evolution of the daily UV index showing higher values in late spring and summer. Thus high erythemal risk values of the UV index (between 7 and 9) occur in 41.6% of the total cases in Badajoz, 41.4% in Cáceres, and 36.6% in Plasencia. These high percentages remark the great interest in reporting values of the UV index in the area of study. Besides the seasonal evolution, cloudiness appears as the main attenuation factor at short‐term scales. Thus spring and autumn presented the highest dispersion because of their great variability in sky conditions. Also, changes in skewness and kurtosis are mainly related to the variability in cloudiness and particularly to the difference between the cloudless summer and the rest of the year. The second objective of the present article is to compare the values of daily UV index as calculated by different approaches: 30‐min average, 10‐min average, and 1‐min average daily maximum erythemal irradiance, and value at solar noon. The results show that although the indices obtained by the different approaches are very similar for cloud‐free days, they show interesting differences for cloudy days. Finally, this paper aims to compare the UV index measured at the mentioned three locations, with the UV index forecasted using the SBDART radiative transfer code and values of total ozone provided by TOMS. The predictions are always calculated assuming cloud‐free conditions. The comparison between experimental and modeled values shows that the forecasted UV index values have an absolute mean error between 7% and 11%, depending on the location and on the delayed daily value of total ozone used as input for the model.

The Information Content of Implied Skewness and Kurtosis Changes Prior to Earnings Announcements for Stock and Option Returns

We explore whether changes in stock return skewness and kurtosis, as implied in option prices preceding earnings announcements, provide information about subsequent stock and option returns through the announcement. We demonstrate that the change in skewness and kurtosis can be related to changing jump risk premiums, where jump risk can be associated with the uncertainty around the direction and size of the stock price response to the earnings announcement. As such, implied skewness (kurtosis) should capture the direction (magnitude) of a stock jump if option prices change as a result of changing jump risk size and intensity. Examining changes in implied skewness and kurtosis preceding over 74,000 earnings announcements for over 4700 firms, we find that both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to skewness. Thus, prior to earnings announcements, option prices contain information about future security returns.

Parameterization of continental boundary layer clouds

Large eddy simulations (LESs) of continental boundary layer clouds (BLCs) observed at the southern Great Plains (SGP) are used to study issues associated with the parameterization of sub‐grid BLCs in large scale models. It is found that liquid water potential temperature θl and total specific humidity qt, which are often used as parameterization predictors in statistical cloud schemes, do not share the same probability distribution in the cloud layer with θl skewed to the left (negatively skewed) and qt skewed to the right (positively skewed). The skewness and kurtosis change substantially in time and space when the development of continental BLCs undergoes a distinct diurnal variation. The wide range of skewness and kurtosis of θl and qt can hardly be described by a single probability distribution function. To extend the application of the statistical cloud parameterization approach, this paper proposes an innovative cloud parameterization scheme that uses the boundary layer height and the lifting condensation level as the primary parameterization predictors. The LES results indicate that the probability distribution of these two quantities is relatively stable compared with that of θl and qt during the diurnal variation and nearly follows a Gaussian function. Verifications using LES output and the observations collected at the Atmospheric Radiation Measurement (ARM) Climate Research Facility (ARCF) SGP site indicate that the proposed scheme works well to represent continental BLCs.

Roughening Due to Ink Jet Rewetting: Effect of Paper Treatment and Composition

An ink jet printer was used to deliver small quantities of ink-dyed water to laboratory handsheets having a range of compositions and treatments. An optical profilometer recorded initial and final roughness statistics at fixed locations on the printed surfaces. For paper made with chemical pulp, it was found that the relative change in local roughness after rewetting (change in roughness divided by initial roughness, ΔR a /R ao ) increased with the degree of calendering, beating, and the amount of surface and internal sizing. The corresponding changes in skewness and kurtosis after rewetting reflected the development of increased fiber rising. Increasing amounts of surface sizing produced larger ΔR a / R ao , corresponding to an increase in the ink penetration depth. Rewetting produced the greatest ΔR a / R ao in paper manufactured with mechanical pulp, with ΔR a /R ao becoming smaller as the fraction of chemical pulp was increased to 0.4, after which it became insensitive to composition.

Application of laser speckle analysis for the assessment of cementitious surfaces subjected to laser cleaning

This paper focuses on the application of laser speckle technique for the assessment of the effectiveness of laser cleaning of cementitious surfaces. Laser speckle-based methods are non-contact, highly resolving techniques for the measurement of displacement, rotation, and strain of an illuminated area on a rough surface. Since the intensity of reflected light depends on the geometrical microstructure and colour of the samples, any alterations of the surface result in different speckle images. Analysis of speckle images presented here is based on the analysis of the distribution of intensity of reflected light obtained in a selected plane, and analysis of statistical parameters describing such distribution (skewness and kurtosis). A wide range of laser-cleaned mortar samples with different geometrical microstructure and moisture content has been subjected to the assessment by He–Ne laser. Laser speckle method has been successfully used to identify the effectiveness of the laser cleaning process with respect to different surface conditions. It appears that the changes in kurtosis and skewness should be mainly associated with the alterations of geometrical microstructure. Whereas, mean light intensity seemed to depend predominantly on the mortar's absorption characteristics (colour).

Nonlinear growth generates age changes in the moments of the frequency distribution: the example of height in puberty

Higher moments of the frequency distribution of child height and weight change with age, particularly during puberty, though why is not known. Our aims were to confirm that height skewness and kurtosis change with age during puberty, to devise a model to explain why, and to test the model by analyzing the data longitudinally. Heights of 3245 Christ's Hospital School boys born during 1927-1956 were measured twice termly from 9 to 20 years (n=129508). Treating the data as independent, the mean, standard deviation (SD), skewness, and kurtosis were calculated in 40 age groups and plotted as functions of age t. The data were also analyzed longitudinally using the nonlinear random-effects growth model H(t)=h(t-epsilon )+alpha, with H(t) the cross-sectional data, h(t) the individual mean curve, and epsilon and alpha subject-specific random effects reflecting variability in age and height at peak height velocity (PHV). Mean height increased monotonically with age, while the SD, skewness, and kurtosis changed cyclically with, respectively, 1, 2, and 3 turning points. Surprisingly, their age curves corresponded closely in shape to the first, second, and third derivatives of the mean height curve. The growth model expanded as a Taylor series in epsilon predicted such a pattern, and the longitudinal analysis showed that adjusting for age at PHV on a multiplicative scale largely removed the trends in the higher moments. A nonlinear growth process where subjects grow at different rates, such as in puberty, generates cyclical changes in the higher moments of the frequency distribution.

K-Hybrid: A Kurtosis-Based Hybrid Thresholding Method for Mechanical Signal Denoising

This paper presents a kurtosis-based hybrid thresholding method, K-hybrid, for denoising mechanical fault signals. The threshold used in the hybrid thresholding method is determined based on kurtosis, which is an important indicator of the signal-to-noise ratio (SNR) of a signal. This together with its sensitivity to outliers and data-driven nature makes a kurtosis-based threshold particularly suitable for on-line detection of mechanical faults featuring impulsive signals. To better reflect the signal composition, the proposed hybrid thresholding rule divides the wavelet transformed input signals into four zones associated with different denoising actions. This alleviates the difficulties present in the simple keep-or-remove and shrink-or-remove approaches adopted by the hard- and soft-thresholding rules. The boundaries of the four zones are on-line adjusted in response to the kurtosis change of the signal. Our simulation results suggest that the mean squared error (MSE) is unable to distinguish the results in terms of the amount of falsely identified impulses. It is therefore inappropriate to use MSE alone for evaluating the denoising results of mechanical signals. As such, a combined criterion incorporating both MSE and false identification power Pfalse is proposed. Our analysis has shown that the proposed K-hybrid approach outperforms the soft, hard, and BayesShrink thresholding methods in terms of the combined criterion. It also compares favorably to the MAP thresholding method for signals with low kurtosis or low SNR. The proposed approach has been successfully applied to noise reduction and fault feature extraction of bearing signals.

The Statistical Computation Underlying Contrast Gain Control

In the early visual system, a contrast gain control mechanism sets the gain of responses based on the locally prevalent contrast. The measure of contrast used by this adaptation mechanism is commonly assumed to be the standard deviation of light intensities relative to the mean (root-mean-square contrast). A number of alternatives, however, are possible. For example, the measure of contrast might depend on the absolute deviations relative to the mean, or on the prevalence of the darkest or lightest intensities. We investigated the statistical computation underlying this measure of contrast in the cat's lateral geniculate nucleus, which relays signals from retina to cortex. Borrowing a method from psychophysics, we recorded responses to white noise stimuli whose distribution of intensities was precisely varied. We varied the standard deviation, skewness, and kurtosis of the distribution of intensities while keeping the mean luminance constant. We found that gain strongly depends on the standard deviation of the distribution. At constant standard deviation, moreover, gain is invariant to changes in skewness or kurtosis. These findings held for both ON and OFF cells, indicating that the measure of contrast is independent of the range of stimulus intensities signaled by the cells. These results confirm the long-held assumption that contrast gain control computes root-mean-square contrast. They also show that contrast gain control senses the full distribution of intensities and leaves unvaried the relative responses of the different cell types. The advantages to visual processing of this remarkably specific computation are not entirely known.

Spectral Moments of the Long-term Average Spectrum: Sensitive Indices of Voice Change After Therapy?

Voice clinicians require an objective, reliable, and relatively automatic method to assess voice change after medical, surgical, or behavioral intervention. This measure must be sensitive to a variety of voice qualities and severities, and preferably should reflect voice in continuous speech. The long-term average spectrum (LTAS) is a fast Fourier transform-generated power spectrum whose properties can be compared with a Gaussian bell curve using spectral moments analysis. Four spectral moments describe features of the LTAS: Spectral mean (Moment 1) and standard deviation (Moment 2) represent the spectrum's central tendency and dispersion, respectively. Skewness (based on Moment 3) and kurtosis (based on Moment 4) represent the spectrum's tilt and peakedness, respectively. To examine whether the first four spectral moments of the LTAS were sensitive to perceived voice improvement after voice therapy, this investigation compared pretreatment and posttreatment voice samples of 93 patients with functional dysphonia using spectral moments analysis. Inspection of the results revealed that spectral mean and standard deviation lowered significantly with perceived voice improvement after successful behavioral management (p < 0.001). However, changes in skewness and kurtosis were not significant. Furthermore, lowering of the spectral mean uniquely accounted for approximately 14% of the variance in the pretreatment to posttreatment changes observed in perceptual ratings of voice severity (p < 0.001), indicating that spectral mean (ie, Moment 1) of the LTAS may be one acoustic marker sensitive to improvement in dysphonia severity.

Evidence that subsistence farmers have domesticated indigenous fruits (Dacryodes edulis and Irvingia gabonensis) in Cameroon and Nigeria

Ten fruit and kernel traits were measured in 152 Irvingia gabonensis and 293 Dacryodes edulis trees from 6 villages in Cameroon and Nigeria. Frequency distribution curves were used to examine the range of variation of each trait of each species in each village and aggregated into national and regional populations. There were differences between the village sub-populations, with regard to the normality (e.g., mean kernel mass of D. edulis) or skewness (e.g., mean flesh depth of D. edulis) of the distribution curves and in the degree of separation between the individual village populations along the x axis, resulting in the development of a bimodal distribution in the regional population. For all traits, populations of both species differed significantly between countries, but only in D. edulis were there significant differences between the Cameroon populations. On the basis of the results of this study, D. edulis can be said to be virtually wild in Nigeria but semi-domesticated in Cameroon, while I. gabonensis is wild in Cameroon and semi-domesticated in Nigeria. These results are discussed with regard to a hypothesis that the range and frequency of variation in the different populations can be used to identify five stages of domestication. From a comparison of the frequency distribution curves of desirable versus undesirable traits, and statistically identifyable changes in skewness and kurtosis, it is concluded that as a result of the farmers’ own efforts by truncated selection, D. edulis is between Stages 2 and 3 of domestication (with a 67% relative gain in flesh depth) in Cameroon, while I. gabonensis in Nigeria is at Stage 2 (with a 44% relative gain in flesh depth). In this study, genetic diversity seems to have been increased, and not reduced, by domestication.

Does the Implied Volatility Flatten Out? Testing with Jensen's Inequality

We develop a simple and fully non-parametric test of concavity of the implied volatility surface to extract a measure of kurtosis of the underlying risk neutral distribution of returns. Using six months of intra day S&P500 data, we find that kurtosis increases with the option's maturity, especially so for short-term options. This is important for pricing and hedging derivatives as it means that the longer the maturity of the option, the more sophisticated the modelling of volatility should be, for example with Levy or GARCH processes. Kurtosis changes sign and may be infinite very close to maturity as concavity becomes ill defined with trading costs killing of trading in the cheaper options. The link between trading costs and concavity suggests that short-run infinite volatility or jump activity may proxy for trading costs.

Tests of Normality Based on Transformed Empirical Processes

The present work introduces four families of tests of normality. The tests in two of them are of the Kolmogorov–Smirnov type, and the tests of the other two are of the Cramer–von Mises type. One family of each type is focused to detect alternatives of skewness and the other one is designed to be specially sensitive to changes in kurtosis. The tests in each family depend on a parameter l: for each integer l, the test statistic involves the computation on the standardized sample points of the Hermite polynomials up to degree l+3. The resulting tests are consistent against all alternative distributions such that at least one of their moments up to order l+3 differ from the corresponding moment of the normal distribution with the same mean and variance. Therefore, a sequence of tests for samples of size n and l=l (n) is consistent against any nonnormal alternative, when limn→∞l(n)=∞. The performance of the proposed tests compares favorably with Shapiro–Wilk and Anderson–Darling omnibus tests, LaRiccia's focused tests, and Kallenberg and Ledwina data driven smooth tests, and the statistics can be easily computed. Hints for their computation are provided.

Multi-moment Approximate Option Pricing Models: A General Comparison (Part 1)

After the seminal paper of Jarrow and Rudd (1982), several authors have proposed to use different statistical series expansion to price options when the risk-neutral density is asymmetric and leptokurtic. Amongst them, one can distinguish the Gram-Charlier Type A series expansion (Corrado and Su, 1996-b and 1997-b), log-normal Gram-Charlier series expansion (Jarrow and Rudd, 1982) and Edgeworth series expansion (Rubinstein, 1998). The purpose of this paper is to compare these different multi-moment approximate option pricing models. We first recall the link between risk-neutral densities and moments in a general statistical series expansion framework. We then derive analytical formulae for these different four-moment approximate option pricing models, namely, the Jarrow and Rudd (1982), Corrado and Su (1996-b and 1997-b) and Rubinstein (1998) models. We investigate in particular the conditions that ensure the respect of the martingale restriction (see Longstaff, 1995) and compare with option pricing models such as Black and Scholes (1973) and Hermite polynomial models (see Madan and Milne, 1994, Abken et al.,1996). We also get for these approximate option pricing models analytical expressions of implied probability distribution, implied volatility smile functions and several hedging parameters of interest, such as the Psi and the Chi that measure respectively the changes in the option price with respect to the changes in kurtosis and skewness.

Impact of the day-of-the-week effect on diversification of exchange rate risks

Diversification and day-of-the-week effects on exchange rate risks have been well documented in the literature, but separately. This paper studies empirically the interaction of diversification and day-of-the-week effects on exchange rate risks. The results show that different days have great impact on diversification of exchange rate risks, particularly on skewness and kurtosis. With an increase in the portfolio size, the average skewness increases on Monday, Thursday and Friday but decreases on Tuesday, Wednesday and Saturday. The average kurtosis decreases with an increase in the portfolio size on Wednesday and Thursday. On the other days, however, the average kurtosis decreases first, and then increases. The results suggest that unsystematic skewness and kurtosis change signs across days of the week. An analysis of consistency over time shows that the portfolio effect on standard deviation is highly stable while the effect on kurtosis is relatively less stable. However, the portfolio effect on skewness is highly unstable over time. Investors should be aware of the day-of-the-week effect on diversification in the foreign exchange markets if they want to maximize their returns and minimize their risks.

Coastal sedimentation associated with the June 2nd and 3rd, 1994 tsunami in Rajegwesi, Java

This paper presents the second detailed study of sediments deposited by modern tusnamis, the first being that of the Flores (Indonesia) tsunami of December 1992 (Shi et al., 1995). Sediment cores were collected from areas in which eyewitnesses reported sediment deposition. Grain size analysis shows pronounced vertical variations in grain size as well as changes in standard deviation, skewness and kurtosis that appear to be indicative of complex tsunami flooding. Vertical variations in grain size in individual cores are greater than spatial variations between cores taken along a transect completed perpendicular to the coastline. The Java tsunami-deposited sediments do not show unequivocal evidence of local erosion but instead evidence for sediment transport and deposition is clear and is characterised by dominantly unimodal sediments with fine-tailed distributions.

Origin of beach ridges and swales

Sandy beach ridges occur in four main categories: (1) Swash-built, (2) Settling lag, (3) Eolian, (4) Storm surge. Ridges in the first two classes are geometrically regular, only a few tens of centimeters above adjacent swales, and commonly in ridge sets and systems (tens to hundreds of ridges each). Individual sets (of 5–25 ridges) tend to stand 0.5 m to 2 m above (or below) adjacent sets. Ridges in the third and fourth classes do not have these characteristics, do not occur in sets, and are generally not suitable for detailed historical studies. No one of these ridges is the same as the storm-built berm, which is almost never preserved. Swash-built sandy beach ridges have diagnostic (1) map spacing, (2) accretion rate, (3) periodicity, (4) crossbedding and (5) granulometry. The last two indicate fair-weather waves on a sandy beach, in contrast with settlinglag ridges (Postma style), which have the same external geometry but which were deposited without important wave work; and in contrast with storm-built berms, generally seen on eroding coasts, but rarely or never in beach ridge plains. The grain-size kurtosis of beach sand is an excellent index to near-shore wave energy density. Changes in kurtosis at ridge set boundaries mark changes in long-term wave energy density, hence in sea level. The latter can be deduced also from set height differences and from spacing differences. Periodicity is typically 30–60 years, map spacing 25–50 m and accretion rate fairly close to 1 m/yr. A few ridge sets, with intervals of 3–7, 10–12, or 18–19 years, have smaller spacings. This is not what can be done, if each ridge is built by one storm. If each ridge had been built by one storm, wide beach ridge plains (like one in Denmark, dating from about 11,700 yr B.P.), would have been formed in the last 30–50 years, at accretion rates of hundreds of meters per year. Instead, each swash-type sandy beach ridge was made by a sea-level rise-and-fall couplet (amplitude, 5–30 cm). The swale marks the lower position. This mechanism reflects the fact that the transverse profile, from beach to sea, is gently concave upward, with maximum curvature close to shore; this is a shape which is out of adjustment with the shoaling wave system shortly after a small sea-level change. Settling-lag ridges were built without waves, hence the ridge-and-swale sequence in this case cannot be attributed to waves, either fair-weather or storm. These ridges show the same historical pattern as do swash-built ridges; this fact suggests that both were controlled by the same mechanism (sea-level change).

Egg Size and Reproductive Allocation in the Pitcherplant Mosquito Wyeomyia smithii (Diptera: Culicidae)

Adult longevity and lifetime fecundity, but not fertility, of northern (Maine, USA) Wyeomyia smithii (Coquillet) increase with female pupal weight. Mean egg size does not vary with pupal weight, but the standard deviation in egg size shows a marginally significant increase with pupal weight. Egg sizes are not skewed but are leptokurtic in their distribution; neither skewness nor kurtosis changes with female pupal weight. Mean egg size is not correlated with weight-specific adult longevity or with weight- and longevity-specific lifetime fecundity. Reproductive effort early in adult life does not affect longevity, reproductive effort late in life, or reproductive rate late in life. Finally, there is no significant correlation late in adult life between weight-specific rate of egg production and the size of eggs being produced. Egg size does vary within females but is not a variable entered into the physiological allocation of resources among survivorship, fecundity, or rate of egg production.

Late Holocene sea-level changes from grain-size data: evidence from the Gulf of Mexico

Grain-size kurtosis of sand in the beach ridge plain of St. Vincent Island, Florida, is numerically reasonably uniform within any one ridge set, but changes at important set boundaries. Where these changes are found, there are also differences in air photo and field appearance and in measured ridge-set heights. Sets with low kurtosis (∼3.0) stand topographically high, and sets with higher values (∼3.6) stand low. Study of wave energy levels and beach sand grain-size kurtosis along modem Gulf of Mexico beaches shows that kurtosis is an inverse function of surf-zone energy density. Storms and storminess (for the study area) can be evaluated in the framework of the selective- transport model of May (1973); the actual data sequence is greatly different from what is required by the model, and therefore storms and storminess cannot be invoked to explain the history of the area. Instead, the data sequence matches results predicted by the model for small sea-level changes. Storms and tectonism do not have appropriate durations and rates of operation, hence did not cause changes in kurtosis across St. Vincent Island. Slow land elevation changes (warping, isostatic adjustment) do not take place repeatedly up and down like the granulometric parameters. Tidal effects, in the study area, are both much too small and too frequent to have been important. The changes in kurtosis therefore indicate water level changes, and provide a sea-level history, including three sea level drops and four rises, of 1-3 m each, since about 3000 BP. Similar results have been obtained elsewhere, so these results are not local.