Cumulative Distribution Function Research Articles

On bid and ask pricing of European options via direct discretization of Choquet distorted expectations

We present a numerical approach to compute bid and ask prices of European options within the conic finance paradigm. In particular, we show how discretizing option bid and ask pricing formulae, where the latter are expressed in terms of Choquet integrals, allows to perform efficient pricing and calibration by means of the COS method and the fast Fourier transform technique. Additionally, the approach introduced provides alternative expressions for risk-neutral European option prices by leveraging the relationship between Choquet and Riemann-Stieltjes integrals. These alternative formulations, requiring only the discretization of the cumulative distribution function of the (transformed) terminal value of the underlying asset, enhance computational efficiency under risk-neutral settings. We provide practical illustrations of the methodology when the underlying asset process follows Heston or Variance Gamma dynamics for both pricing and implied liquidity calculations.

Increased risk of open angle glaucoma in patients with moyamoya disease from a nationwide population-based cohort in Korea

This nationwide population-based retrospective cohort study aims to investigate the association between Moyamoya disease (MMD) and open-angle glaucoma (OAG). In this study using the Korean National Health Insurance Service database, a total of 36,432 patients having diagnostic code with MMD between 2002 and 2022, and their age-, sex-matched non-MMD controls (n = 346,769) were included. We used a Cox proportional hazard model to determine the association between MMD and subsequent OAG after excluding cases with preexisting diagnosis of MMD for the initial 2-year. Kaplan-Meier survival analyses with log-rank test were performed to compare the incidence probability of OAG based on the MMD diagnosis. Cox regression analysis showed that the diagnosis of MMD was associated with increased risk of subsequent diagnosis of OAG (adjusted HR, 1.26; 95% CI, 1.14–1.38; P < 0.001). The cumulative incidence probability of OAG was 3.7% in MMD group and 2.9% in control group at the end of the study period, and was significantly higher among MMD patients than controls consistently during the study period (P < 0.001).In conclusion, the nationwide longitudinal data of Korean population revealed a significant association between MMD and OAG. Presence of MMD may increase the risk of developing OAG.

A more holistic view of the logarithmic dose-response curve offers greater insights into insulin responses

The stimulus-response curve is usually modeled by the Hill function due to its simplicity and clear molecular mechanisms (Michaelis-Menten type of kinetics). Unfortunately, the mechanisms do not explain why the stimulus is ubiquitously measured by logarithmic dose rather than the dose itself and why the log(dose)-response curve possesses such fine properties as symmetry and wide adjustability. Here, the dose response is considered from a holistic perspective spanning multiple biological levels from molecules to the whole organism, which reveals that an appropriate model for log(dose) response is the cumulative normal distribution (CND) function, which had only statistical implication previously but now possess mechanistic-statistical duality. The present CND model establishes a connection between single-cell all-or-none responses and the graded response at the tissue/organism level, reveals the raison d'être of the logarithmic transformation, explains why log(dose)-response curve possesses many fine properties, and reveals new mechanisms of tissue/organism dose-response, including homogeneity-induced sensitivity. It also provides new insights into vital biological processes, such as the insulin dose response.

A Multi-Model Survival Analysis of Lung Cancer Using Parametric Techniques

Lung cancer remains one of the leading causes of cancer-related mortality worldwide, underscoring the critical need for effective prognostic tools. This study utilizes survival analysis to explore the factors that influence the survival outcomes of North Central Cancer Treatment data related to lung cancer. The main goal of this study is to compare and contrast various statistical models, including the Weibull, Exponential, Log-gaussian, Gumbel, and Rayleigh models. We have computed important functions, such as the survival function, the hazard function, and the cumulative hazard function, for all the considered distributions. The Anderson-Darling and Cramer Von-Mises tests, which are Goodness of fit tests, effectively compare and assess various parametric regression survival models. The Weibull survival model is interpreted to be the most effective and efficient way to study the lung cancer dataset, which is concluded upon evaluating the results of Anderson-Darling statistic 0.28745, Cramer Von-Mises statistic 0.0450, Mean Survival Probability 0.9697, Mean Cumulative Survival Probability 0.0303, Akaike Information Criterion 1,650.753 and Bayesian Information Criterion 1623.329 of the Weibull, Exponential, Log-gaussian, Gumbel, and Rayleigh parametric regression survival models.

Effects of sodium-glucose cotransporter-2 inhibitors on chronic kidney disease progression: a multi-state survival model

BackgroundCurrent guidelines recommend good glycemic control in patients with type 2 diabetes (T2D) to limit the progression of associated complications with combination therapies. This study aimed to compare the rate of chronic kidney disease (CKD) progression between patients who did or did not receive sodium-glucose cotransporter-2 inhibitors (SGLT2i) using a multistate model with two intermediate states (i.e., CKD stage 4 (CKD4) and 5 (CKD5)) and one absorbing state (i.e., death).MethodsData from patients with T2D and CKD stage 3 (CKD3) were retrieved for analysis. Patients treated with SGLT2i were matched 1:2 by prescription date with non-SGLT2i patients. The multistate model was constructed from Cox survival regression models specific to each transition stage. Cumulative failure and transition probabilities were estimated from bootstrapping.ResultsData from 6582 patients (2194 and 4388 patients in the SGLT2i and non-SGLT2i groups, respectively) were analyzed. At 10-year follow-up, patients in the SGLT2i group were more likely to remain at CKD3 compared to the non-SGLT2i group: 82.3% (95% CI 79.9%, 84.6%) vs 60.4% (57.6%, 63.4%). Transition probabilities to CKD4, CKD5, and death were lower in the SGLT2i group than non-SGLT2i group: 11.3% (9.5%, 13.3%) vs 19.8% (17.4%, 22.2%), 2.4% (1.5%, 3.4%) vs 7.4% (5.8%, 9.0%), and 4.1% (2.9%, 5.3%) vs 12.4% (10.3%, 14.6%), respectively.ConclusionSGLT2i may delay the decline in renal function and slow CKD progression compared to standard care without SGLT2i.

Risk of Recurrent Ventricular Tachyarrhythmia Following the Occurrence of a First Ventricular Arrhythmic Event in Patients with a Primary Prevention Implantable Cardioverter-Defibrillator

There are limited data on clinical and arrhythmic outcomes following a first ventricular tachyarrhythmia (VTA) in heart failure (HF) patients who receive a primary prevention implantable cardioverter-defibrillator (ICD). To quantify the burden and identify risk factors for recurrent VTA in this population, and to evaluate the risk of all-cause mortality associated with recurrent VTA. The study comprised 789 patients who experienced VTA following primary prevention ICD implantation in 5 ICD trials (MADIT-II, MADIT-RISK, MADIT-CRT, MADIT-RIT, RAID). Landmark analysis was used to quantify the burden and identify predictors of recurrent VTA. Time-dependent analysis was used to evaluate the association of VTA recurrence with subsequent mortality. Among the study patients, mean age was 63 years and 17% were women. The cumulative probability of experiencing at least one recurrent VTA episode at 3 years following a first VTA episode was 60%; the recurrent VTA burden after a first event over 3 years was 2.8 episodes per patient. The risk of recurrent VTA remained ≥56% at 3 years regardless of baseline clinical and echocardiographic risk factors. VTA recurrence was associated with a significant two-fold increased risk of subsequent all-cause mortality. Patients with a primary prevention ICD who experience an episode of VTA are at very high risk of recurrent VTA, regardless of baseline risk factors. Recurrent VTA is associated with a pronounced increase in the risk of death. These findings suggest a need for early intervention following a first VTA in patients who receive a primary prevention ICD.

An improved dynamic-sensitive centrality based on interactive influence for identifying influential nodes in aviation networks

The identification of influential nodes in complex networks is a hot topic among scholars. Classical methods commonly analyze single node information or static structures but seldom emphasize dynamic properties and the interactive influence of nodes. Here, we proposed an improved Dynamic-Sensitive centrality (IDS) method by considering the interactive influence of both the self and neighbor nodes. Based on six real aviation networks and the Susceptible Infected Recovered (SIR) spreading disease model, we simulated the actual spreading process within these networks. Relevant experiments were conducted through Kendall’s correlation coefficient, the imprecision function, and the complementary cumulative distribution function. The experimental results demonstrated that the IDS can more accurately identify the influential node and effectively differentiate the node influence in the network compared with other benchmark methods. Especially in the EU air-2 network, the IDS results in Kendall’s correlation coefficient are improved by 105% compared to the DS centrality.

Outcomes after a virological failure to first-line second-generation INSTI-based therapy in a real-life setting.

Virological failures of first-line second-generation (SG) INSTI-based regimens are rare, usually characterized by low viremia and absence of drug resistance mutations. To explore the efficacy of rescue regimens introduced after virological failure (VF) to a first-line SG-INSTI therapy. This was a retrospective study on people living with HIV (PWH) failing a first-line SG-INSTI regimen [DTG/3TC, BIC/FTC/TAF, DTG-based three-drug regimen (DTG-3DR)] between 24 March 2016 and 31 December 2021. Follow-up accrued from the second viral load (VL) ≥ 50 copies/mL under SG-INSTI regimen (baseline) until virological success (VS, achievement of at least one VL < 50 copies/mL after baseline) or last visit. Cumulative probabilities of VS were estimated by Kaplan-Meier curves and compared using a log-rank test. Overall, of 521 naïve PWH who started a first-line SG-INSTI regimen, 45 (8.6%) had VF after a median of 14.9 (IQR = 6.9-25.9) months: 33/395 (8.4%) individuals failed a DTG-3DR, 11/102 (10.8%) a BIC/FTC/TAF and 1/24 (4.2%) failed a DTG/3TC.At baseline, 12/45 (27%) PWH changed antiretroviral therapy [median baseline VL 134 (IQR = 81-233) copies/mL], while 33 (73%) maintained their failing regimen [median baseline VL 75 (IQR = 60-145) copies/mL].During a median follow-up of 5.13 (IQR = 3.8-7.1) months, 34 (75.6%) PWH achieved VS: 25/33 (75.8%) maintaining their failing regimen, 9/12 (75%) switched regimen; the estimated 6- and 12-months probabilities of VS were 59% and 84%, respectively.There was no difference in VS curves between PWH who maintained their failing regimen and those who switched therapy. Most individuals remained on their failing regimen, achieving spontaneous virological suppression in most cases. These data help to understand a real-life VF scenario in the context of the current SG-INSTI era.

Uplift capacity analysis of inclined strip anchors considering spatial variability of undrained shear strength: RAFELA and ANN

This study investigates the uplift resistance of inclined strip anchors embedded in clays where the undrained shear strength varies spatially. Four input parameters are considered, namely the inclination angle (α), the cover-depth ratio (H/B), the coefficient of variation (COV), and the dimensionless correlation length (Θ) of the undrained shear strength. The random field is modeled using the Random Adaptive Finite Element Limit Analysis (RAFELA) and Monte Carlo simulation in OPTUM G2 under plane strain conditions. The results indicate that COV and Θ significantly affect the shape of probability density function (PDF) and cumulative distribution function (CDF) charts. The probability of failure (PoF) depends evidently on COV and Θ, while H/B and α have lower impacts. The correlation between four inputs and the mean of stability factor (μNc) is depicted through parametric studies. Additionally, Artificial Neural Network (ANN) is implemented to propose a regression model to predict the mean and standard deviation of the stability factor (μNc and σNc). Based on the optimal ANN structure, Permutation Feature Importance (PFI) is applied for the sensitivity analysis, showing that H/B is the most important feature, followed by COV, Θ, and α. The results from this study significantly contribute to the research on the pull-out behavior of strip anchors, particularly in clays with spatial variations in undrained shear strength.

Mathematical Optimization of Wind Turbine Maintenance Using Repair Rate Thresholds

As reliance on wind energy intensifies globally, optimizing the efficiency and reliability of wind turbines is becoming vital. This paper explores sophisticated maintenance strategies, crucial for enhancing the operational sustainability of wind turbines. It introduces an innovative approach to maintenance scheduling that utilizes a mathematical model incorporating an alternating renewal process for accurately determining repair rate thresholds. These thresholds are important for identifying optimal maintenance timings, thereby averting failures and minimizing downtime. Central to this study are the obtained generalized analytical expressions that can be used to predict the total repair time for an observed entity. Four key lemmas are developed to establish formal proofs for the probability density function (PDF) and cumulative distribution function (CDF) of repair rates, both above and below critical repair rate thresholds. The core innovation of this study lies in the methodological application of PDFs and CDFs to set repair time thresholds that refine maintenance schedules. The model’s effectiveness is illustrated using simulated data based on typical wind turbine components such as gearboxes, generators, and converters, validating its potential for improving system availability and operational readiness. By establishing measurable repair rate thresholds, the model effectively prioritizes maintenance tasks, extending the life of crucial turbine components and ensuring consistent energy output. Beyond enhancing theoretical understanding, this research provides practical insights that could inform broader maintenance strategies across various renewable energy systems, marking a significant advancement in the field of maintenance engineering

Rural households' livelihood transitions in China: processes, drivers and outcomes

PurposeThis study aims to comprehensively examine the transitions in household livelihood strategies within rural China, including the underlying processes, drivers and outcomes.Design/methodology/approachThis study uses two waves (2010 and 2018) of longitudinal data from the China Family Panel Studies (CFPS), employing latent cluster analysis, regression models and cumulative distribution function within a dynamic household livelihood strategy framework.FindingsThe results show that (1) households’ livelihood strategies can be categorized into four distinct types, i.e. agricultural dominated, agricultural dominated with non-agricultural supplementation, non-agricultural dominated with agricultural supplementation and employment oriented. (2) During 2010–2018, approximately 60% of households underwent transitions in their livelihoods, encompassing both upward and downward trajectories, with a prevalence of upward transitions. (3) Various forms of livelihood capital significantly contribute to upward transitions, while the availability of land resources and exposure to shocks impede the potential for upward mobility. (4) The transition towards non-agricultural livelihood strategies by households leads to a notable enhancement in their livelihood welfare.Research limitations/implicationsIn the context of urbanization, industrialization and globalization, rural areas in China are undergoing a gradual socioeconomic transformation, which has also led to changes in rural households’ livelihood strategies. Nevertheless, a dearth of empirical investigation exists regarding the dynamics of rural households’ livelihood strategies, the determinants behind such transitions and the resulting outcomes on their livelihoods. A comprehensive understanding of livelihood transitions can provide valuable insights for policymakers in their endeavors to promote rural revitalization in China.Originality/valueBased on the nationwide representative datasets in China, it examines the micro-level livelihood transitions of rural households within the broader context of socioeconomic transformation that presents both opportunities and challenges, as well as vulnerable contexts, shaped by various government policies. This exploration would offer valuable theoretical and empirical evidence to advance our understanding of the process, driver and outcome of rural households’ livelihood transition in developing countries.

An Effective Method for Estimating the Population Mean That Utilizes Dual Auxiliary Information

To improve the effectiveness of population estimators, researchers have recently implemented dual supplementary information. They employed traditional rankings, the empirical cumulative distribution function, and indicator functions as supplementary sources of information in their analysis. An improved family of population mean estimators is introduced in this article, which utilizes the relative ranks of the auxiliary information’s configurations to incorporate the relevant information. A first-order approximation is employed to derive the mathematical expressions for the bias and the mean-squared error (MSE) of the proposed family of estimators. The empirical analysis is investigated to demonstrate the practicality of the proposed estimators in real-world scenarios. Additionally, the theoretical conclusions are effectively validated by the Monte Carlo simulation integration. Our results unequivocally indicate that the proposed family of estimators surpasses their current counterparts.

Maximum non-bounded difference method for overbounding Global Navigation Satellite System errors

Global Navigation Satellite Systems (GNSS) support numerous applications, including mission-critical ones that require high integrity for safe operations such as air, maritime, and land-based navigation. These applications require ensuring the upper bound of the positioning computation, including overbounding any assumptions made in positioning algorithms. One of the main assumptions in the GNSS positioning algorithm is that the error follows a Probability Density Function (PDF), widely assumed to be Gaussian. This assumption should be overbounded to ensure safety. Two mathematical definitions of distribution overbounding have been proposed: Cumulative Distribution Function (CDF) overbounding and paired overbounding. Achieving these definitions has been an open problem for the past 20 years, and to date, no methods have effectively achieved either definition in multimode datasets. This paper proposes the first overbounding method, the Maximum non-Bounded Difference (MnBD) method, capable of achieving both definitions. Its effectiveness is assessed by comparison with the combined CDF bounding and paired overbounding approach. The results show that the MnBD method successfully achieves overbounding in both real datasets and 1000 simulated multimode data, tested on Gaussian and Generalized Extreme Value (GEV) distributions. The latter demonstrates MnBD’s ability to handle asymmetric distributions. The developed approach can be utilized in overbounding the GNSS error at the system level and user level to ensure the system integrity.

Fragility of Highway Embankments Exposed to Permanent Deformations Due to Underlying Fault Rupture

Seismic risk expresses the expected degree of damage and loss following a catastrophic event. An efficient tool for assessing the seismic risk of embankments is fragility curves. This research investigates the influence of embankment’s geometry, the depth of rupture occurrence, and the underlying sandy soil’s conditions on the embankment’s fragility. To achieve this, the response of three highway embankments resting on sandy soil was examined through quasi-static parametric numerical analyses. For the establishment of fragility curves, a cumulative lognormal probability distribution function was used. The maximum vertical displacement of the embankments’ external surface and the fault displacement were considered as the damage indicator and the intensity measure, respectively. Damage levels were categorized into three qualitative thresholds: minor, moderate, and extensive. All fragility curves were generated for normal and reverse faults, as well as the combination of those fault types (dip-slip fault). Finally, the proposed curves were verified via their comparison with those provided by HAZUS. It was concluded that embankment geometry and depth of fault rupture appearance do not significantly affect fragility, as exceedance probabilities show minimal differences (&lt;4%). However, an embankment founded on dense sandy soil reveals slightly higher fragility compared to the one founded on loose sand. Differences regarding the probability of exceedance of a certain damage level are restricted by a maximum of 7%.

Evaluating Meaningful Changes in Patient-Reported Outcome Measurement Information System-Fatigue Scores from Three Phase 3 Clinical Trials of Sarilumab for Patients With Rheumatoid Arthritis.

The aim of this study was to evaluate changes in fatigue measured by Patient-Reported Outcome Measurement Information System (PROMIS)-Fatigue scores in patients with rheumatoid arthritis (RA) who received sarilumab and to assess the proportion of patients achieving clinically meaningful change. Data from three phase 3 randomized controlled trials of patients with RA who received sarilumab-MOBILITY, TARGET, and MONARCH-were evaluated. The 10 RA-relevant items from the 13-item Functional Assessment of Chronic Illness Therapy (FACIT)-Fatigue were scored in the PROMIS T score metric. Mean changes in 10-item PROMIS-Fatigue T score (PROMIS-Fatigue 10a) were compared, proportions of patients reporting meaningful within-person change thresholds were assessed, and results were visualized using empirical cumulative distribution function (eCDF) curves. Patients with RA reported high baseline fatigue. Using PROMIS-Fatigue 10a, at week 24, patients receiving 150 or 200 mg sarilumab every other week in MOBILITY and TARGET had rapidly and significantly improved mean levels of fatigue compared to those who received placebo. When compared to patients who received adalimumab in MONARCH, patients who received sarilumab had a trend toward increased improvement. eCDF curves showed separation between active treatment versus placebo with both sarilumab doses and across the score range for improvement. Higher proportions of patients reported three-, five-, and seven-point improvements in PROMIS-Fatigue scores in groups who received active treatment. Substantial proportions of patients with RA who received sarilumab reported meaningful change in fatigue measured by PROMIS-Fatigue 10a over time. This study demonstrates the ability to convert FACIT-Fatigue score onto the PROMIS T score metric, the rapid reduction in fatigue with biologic therapies, and the use of novel eCDF curves to show individual patient-level change.

Identifying thresholds for meaningful improvements in NTDT-PRO scores to support conclusions about treatment benefit in clinical studies of patients with non-transfusion-dependent beta-thalassaemia: analysis of pooled data from a phase 2, double-blind, placebo-controlled, randomised trial

ObjectivesTo estimate thresholds for defining meaningful within-patient improvement from baseline to weeks 13–24 and interpreting meaningfulness of between-group difference for the non-transfusion-dependent beta-thalassaemia patient-reported outcome (NTDT-PRO) tiredness/weakness (T/W) and shortness...

DUS Topp-Leone-G Family of Distributions: Baseline Extension, Properties, Estimation, Simulation and Useful Applications.

This study introduces the DUS Topp-Leone family of distributions, a novel extension of the Topp-Leone distribution enhanced by the DUS transformer. We derive the cumulative distribution function (CDF) and probability density function (PDF), demonstrating the distribution's flexibility in modeling various lifetime phenomena. The DUS-TL exponential distribution was studied as a sub-model, with analytical and graphical evidence revealing that it exhibits a unique unimodal shape, along with fat-tail characteristics, making it suitable for time-to-event data analysis. We evaluate parameter estimation methods, revealing that non-Bayesian approaches, particularly Maximum Likelihood and Least Squares, outperform Bayesian techniques in terms of bias and root mean square error. Additionally, the distribution effectively models datasets with varying skewness and kurtosis values, as illustrated by its application to total factor productivity data across African countries and the mortality rate of people who injected drugs. Overall, the DUS Topp-Leone family represents a significant advancement in statistical modeling, offering robust tools for researchers in diverse fields.

Skew-Symmetric Generalized Normal and Generalized t Distributions

In this paper, we introduce the skew-symmetric generalized normal and the skew-symmetric generalized t distributions, which are skewed extensions of symmetric special cases of generalized skew-normal and generalized skew-t distributions, respectively. We derive key distributional properties for these new distributions, including a recurrence relation and an explicit form for the cumulative distribution function (cdf) of the skew-symmetric generalized t distribution. Numerical examples including a simulation study and a real data analysis are presented to illustrate the practical applicability of these distributions.

Exponentiated gamma Burr-type X distribution: model, theory, and applications

Several extended Burr-type X distributions have been formed in the past decade. These distributions are widely used in modeling lifetime data as their hazard functions can fit various shapes, such as bathtub, decreasing, and increasing. However, certain extended Burr-type X distributions may not adequately fit the unimodal hazard function. Thus, this paper proposes a new extended distribution with greater flexibility to solve this deficiency: exponentiated gamma Burr-type X distribution. We provide the expressions for the probability density and cumulative distribution functions of the proposed distribution, along with its statistical properties, such as limit behavior, quantile function, moment function, moment-generating function, Renyi entropy, and order statistics. To estimate the model parameters, we employ the maximum likelihood estimation method, and we assess its performance through a simulation study with different sample sizes and parameter values. Finally, to demonstrate the application of this new distribution, we apply it to a real dataset concerning the failure times of aircraft windshields. The results indicate that the new distribution provides a superior fit compared to its submodels and the extended Burr-type X distributions. Moreover, it proves to be highly competitive and can serve as an alternative to certain nonnested models. In summary, the new distribution is highly flexible, capable of modeling a variety of hazard-function shapes, including decreasing, increasing, bathtub, and unimodal patterns.

Bivariate Generalized Exponential Distribution with Positive Probability at (X = 0, Y = 0) and Estimation of Parameters for a Particular Case

Kundu and Gupta, 2009, J Multivar Anal, 100, 581–593, provided a bivariate generalized exponential distribution (BVGED [Formula: see text]), which is a bivariate continuous lifetime distribution. In practice, however, sometimes both the components may fail instantaneously. Thus, we get a mixture bivariate distribution with positive probability at instantaneous failure of each component. The main aim of this article is to define a BVGED with positive probability at instantaneous failure of each component (BVGEDP [Formula: see text]), where PX=0P(X = 0) and P(Y = 0) is a function of parameter [Formula: see text]. It is observed that the joint probability density function and the cumulative distribution function can be expressed in compact forms. Several properties of the distribution have been discussed. For a particular case (BVGEDP ([Formula: see text] 1, 1, 1)), moment type estimators are obtained which are in closed form and maximum likelihood estimators of parameters ([Formula: see text]) are obtained using an iterative procedure. Also, their finite sample and asymptotic properties are discussed using simulation. A final section presents an application to a real data set on which the proposed BVGEDP ([Formula: see text], 1, 1, 1) distribution is fitted. AMS Subject Classification: 62E99