Theoretical Probability Distribution Research Articles

Theoretical probability distribution model and reduction techniques based on an interleaved DFT spread for PAPR in a digital sub-carrier multiplexing system

This paper presents a theoretical probability distribution model for peak-to-average power ratio (PAPR) in the digital sub-carrier multiplexing (DSCM) system, which has not previously been proposed in the literature. To reduce PAPR, an interleaved discrete Fourier transform spread DSCM (I-DFT-S-DSCM) scheme is proposed, which introduces reversible correlations between subcarriers. To investigate the effectiveness of the proposed schemes, a 64-GBaud 16 quadrature amplitude modulation (16-QAM) DSCM system with 4, 8, and 16 sub-carriers was constructed. In the digital domain, the results demonstrate that the proposed theoretical PAPR probability distribution model exhibits mean squared errors (MSE) below 10−5 for the observed and model-predicted complementary cumulative distribution functions (CCDF) in both DSCM and I-DFT-S-DSCM schemes. Regarding PAPR reduction, the I-DFT-S-DSCM scheme demonstrated a reduction in PAPR of up to 1.44 dB compared to the conventional DSCM scheme. To further investigate the impact of PAPR on the bit error rate (BER) performance of the DSCM system, the I-DFT-S-DSCM scheme is implemented with 8 subcarriers transmitted over a 100-km standard single-mode fiber (SSMF). A comparative analysis with DSCM indicates that I-DFT-S-DSCM achieves a PAPR reduction of approximately 1.1 dB and improves receiver sensitivity by approximately 0.7 dB at a 7% hard-decision forward error correction (HD-FEC) threshold, in 100-km single-mode fiber SSMF transmissions.

Bimodalność i długoterminowe trendy wartości ekstremalnych temperatury powietrza

Histograms of air temperature with a bimodal shape are commonly observed in many regions of the world. In this study, we investigate the causes of bimodality in the histograms of daily temperature series (minimum, average, and maximum) for selected climatological stations in Slovakia. Our findings suggest that in the Central European region, the bimodal shape of air temperature histograms is mainly due to the latent heat of freezing, as the surface of snow and ice and the air are thermally coupled. The asymmetry in the air temperature histograms is due to the lower mass heat capacity of ice compared to water and air. The energy-intensive latent heat of conversion of ice to water (and vice versa) results in the more frequent occurrence of ground-layer air temperatures around the freezing point, leading to the formation of the observed local maximum. This has far-reaching implications, such as the calculation of the annual mean air temperature at climatological stations. When calculating the average air temperature, negative temperatures should be given less weight than positive temperatures. Temperatures around 0-6°C should be given higher weight. This may also explain why Arctic regions are experiencing more significant warming than equatorial regions. In the second part of this paper, we analyze the long-term trends of selected temperature indices for the climatological station at Hurbanovo (Slovakia) from 1871 to 2020. Our results indicate statistically significant changes in all temperature indices, with indices related to cold temperatures increasing more significantly than those associated with high temperatures. Finally, study examines theoretical probability distributions to estimate T-year temperatures for temperature indices at the Hurbanovo climate station in Slovakia. The analysis includes three time periods (1901–1960, 1961–2020, and 1991–2020) and reveals significant changes in temperature indices at the Hurbanovo station. The 100-year temperature of TN,min was –35.75°C in 1901–1960, –28.69°C in 1961–2020, and –26.52°C in 1991–2020. The 100-year temperature of TX,max was 39.4°C in 1901–1960 and 39.63°C in 1961–2020. TN,min showed the most significant changes, with the 100-year temperature increasing by up to 7.06°C in 1961–2020 and up to 9.23°C in 1991–2020.

A Routing Model for the Distribution of Perishable Food in a Green Cold Chain

In this research, we develop an extension of the stochastic routing model with a fixed capacity for the distribution of perishable products with a time window. We use theoretical probability distributions to model the life of transported products and travel times in the network. Our main objective is to maximize the probability of delivering products within the established deadline with a certain level of customer service. Our project is justified from the perspective of reducing the pollution caused by greenhouse gases generated in the process. To optimize the proposed model, we use a Generic Random Search Algorithm. Finally, we apply the idea to a real problem of designing strategies for the optimal management of perishable food distribution routes that involve a time window, the objective being to maximize the probability of meeting the time limit assigned to the route problem by reducing, in this way, the pollution generated by refrigerated transport.

Probability distribution functions for the ultimate strength of X-joints with collar plates in compressive load at room and fire conditions

In this paper, the results of performing finite element (FE) analysis on 360 tubular X-joints reinforced with collar plates have been used to propose a probability distribution model for ultimate strength at ambient and fire conditions. As far as the authors know, no study has been conducted on the probability distribution of the ultimate strength in X-joints with collar plates. Consequently, according to the reinforced X-joints, a total of ultimate capacity data sets was generated. The FE models were validated and compared with 35 experimental tests and numerical models. Also, in the present FE models, the welds connecting the plates to the chord member were created. Moreover, the contacts between the outer surfaces of the chord member and the inner surfaces of the reinforcing plates were modeled. In addition, nonlinear material and geometry properties were applied. In the following step, twelve theoretical probability density functions (PDFs) were fitted to relative frequency histograms of five databases. The maximum likelihood method was applied to determine the parameters of each distribution. Investigating the goodness-of-fit according to the Kolmogorov-Smirnov, Anderson Darling, and Chi-square tests showed that the Generalized Petro distribution is the best for the ultimate capacity values in collar plate retrofitted X-joints at ambient and different fire conditions. In the following step, six fully defined theoretical PDFs and cumulative distribution functions (CDFs) were established. Also, probability-probability graphs indicated that the proposed theoretical probability distributions are near the given data sets.

A Design Water Discharge Maxima Forecasting Method Based on Observation Data Using Plotting Position Formulas

Plotting position formulas provide a non-parametric means to estimate the observed hydrological data probability distribution. In particular, using a plotting position formula, a plot of the estimated values from a theoretical parametric probability distribution can be compared with the observation data. It allows an examination of the adequacy of the fit provided by parametric probability distributions. However, results of calculating empirical annual probabilities of exceedance observed maxima water discharges show an increase in the divergence between the estimates obtained using the different plotting position formulas in case of more extreme events. Thereby, the choice of a relevant plotting position formula becomes a challenge. Different plotting position formulas may be admissible options. This article shows that the divergence between the plotting position estimates can be extrapolated to predict design maxima water discharges of low exceedance probabilities.

Extreme wind turbine response extrapolation with the Gaussian mixture model

Abstract. The wind turbine extreme response estimation based on statistical extrapolation necessitates using a minimal number of simulations to calculate a low exceedance probability. The target exceedance probability associated with a 50-year return period is 3.8×10-7, which is challenging to evaluate with a small prediction error. The situation is further complicated by the fact that the distribution of the wind turbine response might be multimodal, and the extremes belong to a different statistical population than the main body of the distribution. Traditional theoretical probability distributions, mostly unimodal, may not be suitable for this task. The problem could be alleviated by applying a fit specifically on the tail of the distribution. Yet, a single unimodal distribution may not be sufficient for modeling diverse wind turbine responses, and an inappropriate distribution model could lead to significant prediction errors, including bias and variance errors. The Gaussian mixture model, a probabilistic and flexible mixture distribution model used extensively for clustering and density estimation tasks, is infrequently applied in the wind energy sector. This paper proposes using the Gaussian mixture model to extrapolate extreme wind turbine responses. The performance of two approaches is evaluated: (1) parametric fitting first and aggregation afterward and (2) data aggregation first followed by fitting. Different distribution models are benchmarked against the Gaussian mixture model. The results show that the Gaussian mixture model is capable of estimating a low exceedance probability with minor bias error, even with limited simulation data, and demonstrates flexibility in modeling the distributions of varying response variables.

The dependence of wave height probability distributions on physical parameters from measurements near Sakhalin Island

The data of long-term surface waves measurements with bottom sensors near Sakhalin Island were used to build instrumental probability distributions for exceedance of wave heights. Waves with heights exceeding the significant wave height by more than three times were recorded. Specific features of the observations conducted during the periods of open and ice-covered sea surfaces are discussed. The subsets of statistically homogeneous data are arranged through selection considering the natural physical dimensionless parameters of the task, that control the effects of finite depth and nonlinearity (namely, the wave steepness, the wave amplitude to water depth ratio, the Ursell parameter). The manifestation of these and composite parameters in theoretical probability distributions of wave heights is discussed. The effects of nonlinearity and the measurement point depth on probability distributions are estimated with a focus on abnormally high waves. In particular, it is shown that for the place of registration an increase in the wave amplitude to water depth ratio parameter leads to a decrease in the probability of abnormally high waves. This behavior is consistent with the Glukhovsky theoretical distribution. The waves characterized by relatively large dimensionless depth parameter exhibit a higher probability of substantial exceedance of the significant height and are better described by the Rayleigh distribution.

Drought Forecasting Using Standard Precipitation Index Based on Rainfall of Western Region

Drought has always been one of the most dangerous natural disasters for manhood. Due to the continuous global climate change, drought occurrences have become more frequent and severe, affecting human existence and long-term social progress. PIStandard values are a measure of the probability of a given precipitation event occurring. They are calculated using a statistical distribution of precipitation data. The three statistical distributions that are most commonly used to model precipitation data are the gamma distribution, the normal distribution, and the log-normal distribution. Therefore, utilising all three of the above-mentioned theoretical probability distributions, the drought index PIStandard has been computed. PIStandard range more than 2 (extremely wet) to less than -2 (extremely dry), with 0.99 to - 0.99 considered the near-normal range. PIStandard is calculated at different time scales which can be 1, 3, 6, 12 and 24 months, time scales. The temporal trends of SPI at the stations were identified using the Mann-Kendall test. PIStandard were computation at 1, 3, 6, 9, 12 and 24-month time scales. PIStandard provides a better analysis of meteorological drought at multiple different timescales for short- and long-term planning because it uses the running sum of rainfall values at 1 to 24 months and more parameters for the statistical distribution used. For short-term drought monitoring and agricultural crop planning, a 1- to 3-month PIStandard can be utilized; however, long-term hydrological drought monitoring and water management planning require PIStandards of 6 to 9 months and 12 to 24 months, respectively. Drought analysis using PIStandard results can be used to design rainwater harvesting and storage structures in drought-affected areas for appropriate crop planning.

Risk management in the allocation of vehicles to tasks in transport companies using a heuristic algorithm

The work deals with the issue of assigning vehicles to tasks in transport companies, taking into account the minimization of the risk of dangerous events on the route of vehicles performing the assigned transport tasks. The proposed risk management procedure based on a heuristic algorithm reduces the risk to a minimum. The ant algorithm reduces it in the event of exceeding the limit, which differs from the classic methods of risk management, which are dedicated only to risk assessment. A decision model has been developed for risk management. The decision model considers the limitations typical of the classic model of assigning vehicles to tasks, e.g. window limits and additionally contains limitations on the acceptable risk on the route of vehicles' travel. The criterion function minimizes the probability of an accident occurring along the entire assignment route. The probability of the occurrence of dangerous events on the routes of vehicles was determined based on known theoretical distributions. The random variable of the distributions was defined as the moment of the vehicle's appearance at a given route point. Theoretical probability distributions were determined based on empirical data using the STATISTICA 13 package. The decision model takes into account such constraints as the time of task completion and limiting the acceptable risk. The criterion function minimizes the probability of dangerous events occurring in the routes of vehicles. The ant algorithm has been validated on accurate input data. The proposed ant algorithm was 95% effective in assessing the risk of adverse events in assigning vehicles to tasks. The algorithm was run 100 times. The designated routes were compared with the actual hours of the accident at the bottom of the measurement points. The graphical interpretation of the results is shown in the PTV Visum software. Verification of the algorithm confirmed its effectiveness. The work presents the process of building the algorithm along with its calibration.

Benford’s Law in Electric Distribution Network

Benford’s law can be used as a method to detect non-natural changes in data sets with certain properties; in our case, the dataset was collected from electricity metering devices. In this paper, we present a theoretical background behind this law. We applied Benford’s law first digit probability distribution test for electricity metering data sets acquired from smart electricity meters, i.e., the natural data of electricity consumption acquired during a specific time interval. We present the results of Benford’s law distribution for an original measured dataset with no artificial intervention and a set of results for different kinds of affected datasets created by simulated artificial intervention. Comparing these two dataset types with each other and with the theoretical probability distribution provided us the proof that with this kind of data, Benford’s law can be applied and that it can extract the dataset’s artificial manipulation markers. As presented in the results part of the article, non-affected datasets mostly have a deviation from BL theoretical probability values below 10%, rarely between 10% and 20%. On the other side, simulated affected datasets show deviations mostly above 20%, often approximately 70%, but rarely lower than 20%, and this only in the case of affecting a small part of the original dataset (10%), which represents only a small magnitude of intervention.

Best Fitting of Probability Distribution for Monthly and Annual Maximum Rainfall Prediction in Junagadh Region (Gujarat-India)

Rain is a meager and crucial hydrological variable in arid and semi-arid region. Junagadh (Gujarat-India) reels under monsoon rainfall uncertainties and thereby the agriculture and other water resources management activities suffer. Therefore, urgent attention is needed to address water resources conservation and crop damage issues due to deficits or excess rainfall. Water resources development of any locality depends on amount of runoff generated and rainfall received. Appropriate probability distributions need to be selected and fitted to the historical time series of rainfall for better frequency analysis and forecasting of the rainfall. The daily rainfall data was collected for a period of 38 years i.e., from 1984 to 2021. This research attempts to fit eightdifferent theoretical probability distributions to the monthly and annual maximum rainfall for one to five consecutive days to select the best one for the better prediction of maximum rainfall. For determination of goodness of fit Chi-Square and Nash-Sutcliffe Efficiency were carried out by comparing the expected values with the observed values. The results indicated that the Gumbel distribution emerged to be the best fit for the prediction of monthly and annual maximum rainfall of Junagadh Region.

Testing a numerically-analytical method for prediction design maxima discharges of floods using plotting position formulas: the river Uzh case, the “Uzhhorod” gauging station data

There are a lot of analytical probability distributions that might be used to predict peak discharges of floods. However, there is no proper theoretical or another similar justification for choosing an appropriate parametric probability distribution to predict peak discharges of floods by using observed data. As a permissible hypothesis, any of recommended probability distributions can be considered providing it meets the given statistical criteria and other considerations for the adequacy of simulation are taken into account. In turn, more than seventeen plotting position formulas have been proposed. They provide a non-parametric means to estimate the observed data probability distribution. Using a plotting position formula, a plot of the estimated values from a theoretical parametric probability distribution can be compared with the observed data.The choice of a better plotting position formula for fitting the different probability distributions has been discussed many times in hydrology and statistical literature. However, no specific criterion for choosing these formulas has been proposed yet. Perhaps there is no need for such a criterion. Maybe, the diversity of estimates that can be obtained due to these formulas matters more. Due to the diversity of the different plotting position estimates, from the point of view of informational entropy, different plotting position formulas enable revealing epistemic (non-stochastic or subjective) uncertainty in predictions of hydrological extremes.Results of calculating empirical annual probabilities of exceedance observed maxima discharge employing various plotting position formulas show that increasing the predicting horizon toward low probable and more extreme events increases the divergence between the estimates obtained using the different plotting position formulas. Therefore, it is reasonable to assume that this divergence may be extrapolated to predict design maxima discharges of floods based on empirical estimates of plotting position probabilities.This paper proposes a numerically-analytical method using such an extrapolation. It is based on using different plotting position formulas, numerical calculations of plotting position probabilities, and extrapolation of the divergence between the obtained estimates. The method is tested in predicting the maxima discharges of 0.5% and 1% annual probability of exceedance for the Uzh River flowing in the Transcarpathia region, the hydrological station “Uzhhorod” data.

Frequency analysis of rainfall events in Karbala city, Iraq, by creating a proposed formula with eight probability distribution theories

ABSTRACT Due to its impact on the derivation of hydrological models and the safe design of sewer and storm networks, the anticipation of rainfall events should be intensively studied. In this regard, studying the rainfall events in Karbala, Iraq, has specific importance after the rapid increase in population in this city and the impact of climate change beyond 2003. Herein, the maximum daily rainfall depth of Karbala city has been analyzed to investigate and extract its probability of future occurrence using frequency analysis. Eight theoretical probability distributions, which are Weibull, Gamma, Gumbel, Log normal, Generalized Extreme Value, Normal, Exponential, and Log-Pearson Type III, were fitted using Hyfran Plus software to simulate the characteristics of the observed probability of rainfall depth. Based on the results of four statistical indicators, the exponential distribution revealed the best performance as compared with other distributions. Accordingly, ‎the synthetic storms of 24 hr were derived‎ for cumulative and incremental distribution of rainfall depth using the Soil Conservation Service method type ΙΙ for the arid and semiarid region to recurrence periods ‎‎(T = 2, 5, 10, 15, 25, 50, 100, 200, and 500), also the rainfall intensity duration frequency curves were developed. As an essential finding, new validated empirical formula has been proposed to optimize the coefficients of the location of Karbala city which may fill the gap for predicting the rainfall intensity and improving storm management strategies in Iraq.

Dine-Fischler-Srednicki-Zhitnitsky-type axions and where to find them

We systematically calculate the axion-photon coupling for non-minimal DFSZ models. Thereby we can classify every calculated model and study the resulting distributions, relevant for axion experiments like haloscopes, helioscopes or light-shining-through-a-wall experiments. By adding more than one additional Higgs doublet, these non-minimal DFSZ models extend the viable axion parameter space and lead to a large range of axion-photon couplings. We find couplings almost three orders of magnitude larger than the ones of the minimal models. Most of the possible axion-photon couplings, however, lie in the vicinity of the values dictated by the minimal models. We quantify this by introducing a theoretical prior probability distribution for DFSZ-type axions and giving $68\%$ and $95\%$ lower bounds as well as two-sided bands. We compare our results for the DFSZ axion-photon coupling distributions with the KSVZ case, for which a similar analysis has been conducted. Both display similar values as well as a very specific pattern. In order to identify preferred models, we discuss the role of flavour changing neutral currents and the domain wall problem as possible selection criteria. It is possible to construct a large number of non-minimal DFSZ models with a domain wall number of unity and thereby avoiding the domain wall problem. This subset also has a significantly enhanced axion-photon coupling compared to the minimal DFSZ models.

Quantification of Equivalent Strut Modeling Uncertainty and Its Effects on the Seismic Performance of Masonry Infilled Reinforced Concrete Frames

ABSTRACT Quantifying aleatory and epistemic uncertainty in nonlinear structural response simulation is key to robust performance-based seismic assessments. This paper focuses on the modeling parameters that are used to describe the nonlinear force-deformation response of the equivalent infill struts used in models of reinforced concrete frames with infills. The variability in several parameters is characterized by developing empirical and theoretical multivariate probability distributions based on the deduced-to-predicted ratios derived using data from 113 physical experiments. The effect of the uncertainty in the infill strut modeling parameters on maximum story drift ratios and associated limit state fragility functions is investigated for a 3-story reinforced concrete frame building with infills. Multiple stripe analysis is performed using hazard-consistent ground motions. Relative to when only record-to-record variability is considered, modeling parameter uncertainty has a non-negligible effect on the dispersion of the maximum story drift ratios, and affects both the median and dispersion of the limit state fragilities.

Modelling and assessment of the arrival and departure process at the terminal area: A case study of Chennai international airport

Airport and terminal area traffic congestion is a growing concern of the air traffic management (ATM) system. A major step towards mitigating the impacts of congestion is understanding the fluctuating arrival and departure process at airports. Exploring the intrinsic time-varying nature of the arrival and departure process enhances this understanding, hence, is instrumental in formulating operational policies for managing airport capacity and delays. This paper presents a data-driven statistical framework to investigate, understand, and model the time-varying fluctuations in the aircraft arrival and departure process. We have considered one-month data obtained from Chennai international airport operations for this study. The dynamic evolution and fluctuation characteristics of arrivals and departures are conducted using Seasonality and Multifractal Detrended Fluctuation Analysis. Six theoretical probability distributions were used to fit the observed aircraft arrivals and departures at different temporal scales using the maximum likelihood estimation method. This study also develops a G1(t)/G2(t)/KFirst Come First Serve dynamic queuing model for a day’s arrival and departure process. The results suggest that arrival and departure processes exhibit weak but visible multifractal characteristics. Fluctuations are higher at a smaller temporal scale compared to a larger scale, and the probability distributions of arrival and departure are also time-varying. The framework has universal applicability, and the insights have important implications for operational policies on the air transportation workforce and infrastructure management.

Probability distribution models for the ultimate strength of tubular T/Y-joints reinforced with collar plates at room and different fire conditions

In this research work, the simulation results of 360 T/Y-joints reinforced with collar plates have been used to propose theoretical probability distribution models for the ultimate capacity at ambient and fire conditions. So far, no study has been carried out on the probability distribution of ultimate strength in joints with collar plates at room or elevated temperature. Therefore, according to the reinforced T/Y-joint models, which were verified with 18 tests, a total of ultimate capacity data sets was produced. In the FE models, the welds along the collar/brace intersection and between the chord and collar have been generated. Also, the Augmented Lagrange method was applied as the contact algorithm for solving the contact between the collar and chord. In the next step, 13 theoretical probability density functions (PDFs) were fitted to the relative frequency histograms of the databases. For obtaining the parameters of each distribution, the maximum likelihood (ML) method was utilized. Assessing the goodness-of-fit based on the Kolmogorov-Smirnov and Anderson Darling tests indicated that the Johnson SB distribution is the best for the ultimate capacity values in the T/Y-joints reinforced with collar plates at 20, 400, 600, and 800 °C. But, for the reinforced joints at 200 °C, the Inverse Gaussian (3P) distribution is the best. In the next step, five fully defined theoretical PDFs were proposed for the collar plate reinforced T/Y-joints at room and different high temperatures. Probability difference and probability-probability graphs indicated that the proposed theoretical probability distributions are well near the given data sets.

The Seoul Neuropsychological Screening Battery (SNSB) for Comprehensive Neuropsychological Assessment.

The Seoul Neuropsychological Screening Battery (SNSB) is known as a representative comprehensive neuropsychological evaluation tool in Korea since its first standardization in 2003. It was the main neuropsychological evaluation tool in the Clinical Research Center for Dementia of South Korea, a large-scale multi-center cohort study in Korea that was started in 2005. Since then, it has been widely used by dementia clinicians, and further solidified its status as a representative dementia evaluation tool in Korea. Many research results related to the SNSB have been used as a basis for the diagnosis and evaluation of patients in various clinical settings, especially, in many areas of cognitive assessment, including dementia evaluation. The SNSB version that was updated in 2012 provides psychometrically improved norms and indicators through a model-based standardization procedure based on a theoretical probability distribution in the norm's development. By providing a score for each cognitive domain, it is easier to compare cognitive abilities between domains and to identify changes in cognitive domain functions over time. Through the development of the SNSB-Core, a short form composed of core tests, which also give a composite score was provided. The SNSB is a useful test battery that provides key information on the evaluation of early cognitive decline, analysis of cognitive decline patterns, judging the severity of dementia, and differential diagnosis of dementia. This review will provide a broad understanding of the SNSB by describing the test composition, contents of individual subtests, characteristics of standardization, analysis of the changed standard score, and related studies.

Discussion on Reasonable Flow Pressure in Class I Block of A Oilfield

Reasonable flow pressure is the premise to ensure the maximum production capacity of oil wells. After years of development and adjustment, the adaptability of pump depth and flow pressure needs to be further studied, so as to formulate a reasonable flow pressure under the current development situation. This paper studies the relationship between flow pressure and production in a class of blocks by using theoretical research and data probability distribution method, determines the current reasonable flow pressure system in line with the actual situation, and proposes the test potential wells for adjustment

Efficient sampling of the irregular probability distributions of geotechnical parameters for reliability analysis

Values of site-specific geotechnical parameters are generally estimated based on the results of in-situ and/or laboratory tests. In most cases, the field test data in geotechnical engineering practice are so limited and sparse that their histograms may only be described using an irregular probability distribution. In addition, the posterior distributions of geotechnical parameters obtained from the Bayesian updating may also be an irregular probability distribution. The irregular probability distributions that exhibit a multi-modal nature cannot be well fitted using theoretical probability distributions such as normal, lognormal or beta distributions. Therefore, challenges may arise in sampling of such irregular probability distributions, which could hinder the subsequent geotechnical reliability analyses. To facilitate the geotechnical reliability analyses with limited data, an efficient sampling method that is based on a mixture of uniform distributions is proposed in this study. This sampling method is capable of drawing random samples from the irregular probability distribution of a single geotechnical parameter as well as the joint probability distribution of cross-correlated spatially varied geotechnical parameters. The proposed sampling method is first illustrated and validated using three examples that employ both simulated and real data. The results confirm that the proposed sampling method is accurate and highly efficient. Last, the proposed method is implemented to sample from the posterior distributions of two cross-correlated spatially varied geotechnical parameters obtained from the Bayesian updating of a soil slope. The results indicate that the proposed method can provide an effective and versatile tool for the random sampling of the joint probability distribution and posterior distributions of geotechnical parameters.