Search

The study of analytical solutions for the bearing capacity of reinforced soil foundations is a very important topic in engineering mathematics. Existing evaluations of the foundation-bearing capacity on reinforced soils are based on dry conditions, while many foundations are located on unsaturated soils in real engineering. In this paper, a new formula for the bearing capacity of reinforced strip footings on unsaturated soils is presented. Two sliding failure mechanisms are constructed based on the position of the reinforcement layer relative to the sliding surface. The distribution of apparent cohesion in the depth direction is calculated by considering the effect of matrix suction. By additionally considering the work conducted by the reinforcement and the contribution of the apparent cohesion, the bearing capacity formula is obtained using the upper bound theorem of limit analysis. The bearing capacity solution is obtained by adopting the sequential quadratic programming (SQP) algorithm. Comparing the results under two failure mechanisms, the optimal bearing capacity and the optimal embedment depth of reinforcement are obtained. The results of this paper are consistent with those of the existing literature. Finally, the effects of reinforcement embedment depth, effective internal friction angle, uniform load, and unsaturated soil parameters on the optimal bearing capacity are investigated through parametric analysis. This paper provides useful recommendations for the engineering application of reinforced strip footings on unsaturated soils. [ABSTRACT FROM AUTHOR]

This paper proposes an upper bound for mine productivity (useful for long-term planning) and also a simple truck dispatch rule (useful for short-term operations) that demonstrates how tight the upper bound can be using a simulation. It also proposes a greedy search to approximate the productivity upper bound, which is faster and often exact. Uncertainty is added to the simulation in order to verify how the productivity responds to it. Typically, the productivity's upper bound is less tight close to its saturation point as a function of the number of trucks, where adding more trucks only increases queues. Furthermore, more uncertainty in the model typically leads to a less tight upper bound. The results conducted using real data from an open pit mine in Brazil show that the gap between the productivity upper bound and the productivity realization using the proposed dispatch rule for a homogeneous fleet can be less than 2% , but it can be as large as 12% near the productivity saturation point without uncertainty. Even though this gap seems to become arbitrarily small as the number of trucks and the simulation horizon increase, the productivity upper bound is never violated, which validates it as an upper bound and induces optimality for the dispatch rule. [ABSTRACT FROM AUTHOR]

Label corruption leads to a significant challenge in supervised learning, particularly in deep neural networks. This paper considers recovering a small corrupted subset of data samples which are typically caused by non-expert sources, such as automatic classifiers. Our aim is to recover the corrupted data samples by exploiting a finite query-testing system as an additional expert. The task involves identifying the corrupted data samples with minimal expert queries and finding them to their true label values. The proposed query-testing system uses a random selection of a subset of data samples and utilizes finite field operations to construct combined responses. In this paper, we demonstrate an information-theoretic lower bound on the minimum number of queries required for recovering corrupted labels. The lower bound can be represented as a function of joint entropy with an imbalanced rate of data samples and mislabeled probability. In addition, we find an upper bound on the error probability using maximum a posteriori decoding. [ABSTRACT FROM AUTHOR]

In this paper, we study the class of graphs G m , n that have the same degree sequence as two disjoint cliques K m and K n , as well as the class G ¯ m , n of the complements of such graphs. The problems of finding a maximum clique and a maximum independent set are NP-hard on G m , n . Therefore, looking for upper and lower bounds for the clique and independence numbers of such graphs is a challenging task. In this article, we obtain such bounds, as well as other related results. In particular, we consider the class of regular graphs, which are degree-equivalent to arbitrarily many identical cliques, as well as such graphs of bounded degree. [ABSTRACT FROM AUTHOR]

The Resource-Constrained Project Scheduling Problem (RCPSP) is a significant and important issue in the field of project management. It arises during project planning when resources must be allocated among tasks with specific time constraints. Solving this problem enables the optimization of project execution time, minimization of resource costs, and increased efficiency of the entire team's work. Due to the increasing complexity of projects, the development of new methods and algorithms to solve RCPSP is relevant nowadays. The existing methods for obtaining approximate solutions with guaranteed accuracy are characterized by high computational complexity and are often ineffective in considering the specific constraints of the problem. Fast heuristic approaches also have several drawbacks related to fine-tuning algorithm parameters and strong dependence on the quality of the initial solution. This paper investigates the features of the linear integer programming (LIP) model to solve RCPSP. The proposed LIP model is universal and scalable, enabling it to fully consider all specific aspects of the problem. The paper provides a construction algorithm of a functional space of the model and discusses the estimation of complexity. From the estimation of the mentioned algorithm's complexity, it is observed that the general complexity of the proposed approach is proportional to a controlled parameter of the LIP. Increasing this controlled parameter can significantly reduce the dimensionality of the initial problem, thus leading to the effectiveness of the LIP model-based approach in terms of computational resources. An upper bound for the value of this parameter is obtained for a special case of the RCPSP. Using the obtained balanced value, a numerical experiment was carried out on real-world samples. [ABSTRACT FROM AUTHOR]

In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity. [ABSTRACT FROM AUTHOR]

The yield criterion of many metallic materials differs from the von Mises yield criterion. However, the available upper bound solutions are almost all restricted to this criterion. The objective of the present paper was to derive an upper bound solution based on a generalized yield criterion for evaluating the extrusion and drawing force, assuming a conical die. The solution method differs from the conventional method used in conjunction with the von Mises yield criterion. The development of this method is necessary, since the work function is not readily expressed as an explicit function of strain rate invariants if the generalized yield criterion is adopted. The solution is illustrated using numerical examples, which show the effect of the yield criterion on the limit load. [ABSTRACT FROM AUTHOR]

Radio antennas switch signals in the form of radio waves using different frequency bands of the electromagnetic spectrum. To avoid interruption, each radio station is assigned a unique number. The channel assignment problem refers to this application. A radio geometric mean labeling of a connected graph G is an injective function h from the vertex set, V (G) to the set of natural numbers N such that for any two distinct vertices x and y of G , h (x) · h (y) ≥ d i a m + 1 − d (x , y) . The radio geometric mean number of h , r g m n (h) , is the maximum number assigned to any vertex of G. The radio geometric mean number of G, r g m n (G) is the minimum value of r g m n (h) , taken over all radio geometric mean labeling h of G . In this paper, we present two theorems for calculating the exact radio geometric mean number of paths and cycles. We also present a novel algorithm for determining the upper bound for the radio geometric mean number of a given graph. We verify that the upper bounds obtained from this algorithm coincide with the exact value of the radio geometric mean number for paths, cycles, stars, and bi-stars. [ABSTRACT FROM AUTHOR]

In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate dynamic hedging strategy. We test the approach on different specifications of a Bermudan max-call option. In all cases it produces highly accurate prices and dynamic hedging strategies with small replication errors. [ABSTRACT FROM AUTHOR]

This paper proposes an improved interval fuzzy modeling (imIFML) technique based on modified linear programming and actual boundary points of data. The imIFML technique comprises four design stages. The first stage is based on conventional interval fuzzy modeling (coIFML) with first-order model and linear programming. The second stage defines reference lower and upper bounds of data using MATLAB. The third stage initially adjusts scaling parameters in the modified linear programming. The last stage automatically fine-tunes parameters in the modified linear programming to realize the best possible model. Lower and upper bounds approximated by the imIFML technique are closely fitted to the reference lower and upper bounds, respectively. The proposed imIFML is thus significantly less conservative in cases of large variation in data, while robustness is inherited from the coIFML. Design flowcharts, equations, and sample MATLAB code are presented for reference in future experiments. Performance and efficacy of the introduced imIFML are evaluated to estimate solar photovoltaic, wind and battery power in a demonstrative renewable energy system under large data changes. The effectiveness of the proposed imIFML technique is also compared with the coIFML technique. [ABSTRACT FROM AUTHOR]

This paper presents the analytical method capacity of the upper bound theorem, under modular approach, to extend its application possibilities. Traditionally, this method has been applied in forging processes, considering plane strain condition and parts with double symmetry configuration. However, in this study, the double symmetry is eliminated by means of a fluency plane whose position comes from the center of mass calculated. The study of the load required to ensure the plastic deformation will be focus on the profile of the part, independently on both sides of the fluence plane, modifying the number and the shape of the modules that form the two halves in which the part is defined. This way, it is possible to calculate the necessary load to cause the plastic deformation, whatever its geometric profile. [ABSTRACT FROM AUTHOR]

The objective of this work is to analyze the importance of the product λ ′ (0) ρ ′ (1) in determining low density parity check (LDPC) code performance, as far as its influence on the weight distribution function and on the decoding thresholds. This analysis is based on the 2006 paper by Di et al., as far as the weight distribution function is concerned, and on the 2018 paper by Vatta et al., regarding the LDPC decoding thresholds. In particular, the first paper Di et al. analyzed the relation between the above mentioned product and the minimum weight of an ensemble of random LDPC codewords, whereas in the second some analytical upper bounds to the LDPC decoding thresholds were determined. In the present work, besides analyzing the performance of an ensemble of LDPC codes through the outcomes of Di et al.'s 2006 paper, we give the relation between one of the upper bounds found in Vatta et al.'s 2018 paper and the above mentioned product λ ′ (0) ρ ′ (1) , thus showing its role in also determining an upper bound to LDPC decoding thresholds. [ABSTRACT FROM AUTHOR]

The distribution of eigenvalues and the upper bounds for the spread of interval matrices are significant in various fields of mathematics and applied sciences, including linear algebra, numerical analysis, control theory, and combinatorial optimization. We present the distribution of eigenvalues within interval matrices and determine upper bounds for their spread using Geršgorin's theorem. Specifically, through an equality for the variance of a discrete random variable, we derive upper bounds for the spread of symmetric interval matrices. Finally, we give three numerical examples to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

An upper bound analysis of free-chip machining has been carried out, where the tool cutting and friction forces were determined from the deformation energy dissipated during the chip separation process. The method employed was based on the classical upper bound theorem, as formulated by Prager and Hodge, and Drucker, Prager, and Greenberg, and its modification by Collins, to deal with the metal forming processes involving coulomb friction. A straight shear plane and coulomb friction at the chip/tool interface were assumed and the energy required for cutting was calculated from a strain rate/velocity field that was constructed using the method proposed by Collins. Cutting forces, thrust forces, tool/chip contact lengths, and chip thickness ratios were determined for different tool rake angles and friction conditions. The theoretical results were also compared with some experimental results that are available in the published literature. The comparison between the two was not found to be satisfactory. This may be due to the non-unique nature of the machining process, as stated by Hill and demonstrated by other authors. The results calculated from the present method of "energy balance" were also found to be in agreement with those obtained by Merchant using the principle of "force balance". [ABSTRACT FROM AUTHOR]

The evaluation of the bearing capacity of strip footings generally assumes that the soil is either dry or fully saturated, which contradicts the actual condition in nature where the soil is often in a partially saturated state. Furthermore, infiltration has a significant impact on the shear strength of the soil. Following the upper bound theory of the limit analysis, this article provides a theoretical framework for assessing the bearing capacity under transient flow with linear variation in infiltration intensity for the first time. Firstly, the closed form of suction stress under linear transient infiltration is derived using Laplace transform and introduced into the Mohr–Coulomb criterion. A discrete failure mechanism with fewer variables and higher accuracy is provided to ensure kinematic admissibility. The upper bound solution for bearing capacity is obtained by solving the power balance equation. The present results are compared with results from the published literature and the finite element, confirming the validity and superiority of the theoretical framework provided. A parametric analysis is also conducted on three hypothetical soil types (fine sand, silt, and clay), and the results show that unsaturated transient infiltration has a positive influence on increasing the foundation bearing capacity. The magnitude of the influence is comprehensively controlled by factors such as soil type, saturated hydraulic conductivity, infiltration intensity, infiltration time, and water table depth. The increase in bearing capacity due to unsaturated transient infiltration can be incorporated into Terzaghi's equation as a separate component presented in tabular form for engineering design purposes. [ABSTRACT FROM AUTHOR]

Complex networks analysis (CNA) has attracted so much attention in the last few years. An interesting task in CNA complex network analysis is community detection. In this paper, we focus on Local Community Detection, which is the problem of detecting the community of a given node of interest in the whole network. Moreover, we study the problem of finding local communities of high density, known as α-quasi-cliques in graph theory (for high values of α in the interval ]0,1[). Unfortunately, the higher α is, the smaller the communities become. This led to the maximal α-quasi-clique community of a given node problem, which is, the problem of finding local communities that are α -quasi-cliques of maximal size. This problem is NP-hard, then, to approach the optimal solution, some heuristics exist. When α is high (>0.5) the diameter of a maximal α -quasi-clique is at most 2. Based on this property, we propose an algorithm to calculate an upper bound to approach the optimal solution. We evaluate our method in real networks and conclude that, in most cases, the bound is very accurate. Furthermore, for a real small network, the optimal value is exactly achieved in more than 80% of cases. [ABSTRACT FROM AUTHOR]

Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We present the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy are presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric. Finally, we predict nucleosome positioning of fly and yeast based on generalized relative entropy and relative entropy respectively. The experimental results show that the properties of generalized relative entropy are better than relative entropy. [ABSTRACT FROM AUTHOR]

A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance. [ABSTRACT FROM AUTHOR]

Quantum coherence is an important physical resource in quantum information science, and also as one of the most fundamental and striking features in quantum physics. To quantify coherence, two proper measures were introduced in the literature, the one is the relative entropy of coherence C r (ρ) = S (ρ diag) − S (ρ) and the other is the ℓ 1 -norm of coherence C ℓ 1 (ρ) = ∑ i ≠ j | ρ i j | . In this paper, we obtain a symmetry-like relation of relative entropy measure C r (ρ A 1 A 2 ⋯ A n ) of coherence for an n-partite quantum states ρ A 1 A 2 ⋯ A n , which gives lower and upper bounds for C r (ρ) . As application of our inequalities, we conclude that when each reduced states ρ A i is pure, ρ A 1 ⋯ A n is incoherent if and only if the reduced states ρ A i and tr A i ρ A 1 ⋯ A n (i = 1 , 2 , ... , n) are all incoherent. Meanwhile, we discuss the conjecture that C r (ρ) ≤ C ℓ 1 (ρ) for any state ρ , which was proved to be valid for any mixed qubit state and any pure state, and open for a general state. We observe that every mixture η of a state ρ satisfying the conjecture with any incoherent state σ also satisfies the conjecture. We also observe that when the von Neumann entropy is defined by the natural logarithm ln instead of log 2 , the reduced relative entropy measure of coherence C ¯ r (ρ) = − ρ diag ln ρ diag + ρ ln ρ satisfies the inequality C ¯ r (ρ) ≤ C ℓ 1 (ρ) for any state ρ. [ABSTRACT FROM AUTHOR]

In this paper, we obtain upper bounds on the minimum distance for turbo codes using fourth degree permutation polynomial (4-PP) interleavers of a specific interleaver length and classical turbo codes of nominal 1/3 coding rate, with two recursive systematic convolutional component codes with generator matrix G = [ 1 , 15 / 13 ] . The interleaver lengths are of the form 16 Ψ or 48 Ψ , where Ψ is a product of different prime numbers greater than three. Some coefficient restrictions are applied when for a prime p i ∣ Ψ , condition 3 ∤ (p i − 1) is fulfilled. Two upper bounds are obtained for different classes of 4-PP coefficients. For a 4-PP f 4 x 4 + f 3 x 3 + f 2 x 2 + f 1 x (mod 16 k L Ψ) , k L ∈ { 1 , 3 } , the upper bound of 28 is obtained when the coefficient f 3 of the equivalent 4-permutation polynomials (PPs) fulfills f 3 ∈ { 0 , 4 Ψ } or when f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { (4 k L − 1) · Ψ , (8 k L − 1) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. The upper bound of 36 is obtained when the coefficient f 3 of the equivalent 4-PPs fulfills f 3 ∈ { 2 Ψ , 6 Ψ } and f 2 ∈ { (2 k L − 1) · Ψ , (6 k L − 1) · Ψ } , k L ∈ { 1 , 3 } , for any values of the other coefficients. Thus, the task of finding out good 4-PP interleavers of the previous mentioned lengths is highly facilitated by this result because of the small range required for coefficients f 4 , f 3 and f 2 . It was also proven, by means of nonlinearity degree, that for the considered inteleaver lengths, cubic PPs and quadratic PPs with optimum minimum distances lead to better error rate performances compared to 4-PPs with optimum minimum distances. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic multi-task scheduling prototype is proposed to improve the limited resource utilization in the vehicular networks (VNET) assisted by mobile edge computing (MEC). To ensure quality of service (QoS) and meet the growing data demands, multi-task scheduling strategies should be specially constructed by considering vehicle mobility and hardware service constraints. We investigate the rational scheduling of multiple computing tasks to minimize the VNET loss. To avoid conflicts between tasks when the vehicle moves, we regard multi-task scheduling (MTS) as a multi-objective optimization (MOO) problem, and the whole goal is to find the Pareto optimal solution. Therefore, we develop some gradient-based multi-objective optimization algorithms. Those optimization algorithms are unable to deal with large-scale task scheduling because they become unscalable as the task number and gradient dimensions increase. We therefore further investigate an upper bound of the loss of multi-objective and prove that it can be optimized in an effective way. Moreover, we also reach the conclusion that, with practical assumptions, we can produce a Pareto optimal solution by upper bound optimization. Compared with the existing methods, the experimental results show that the accuracy is significantly improved. [ABSTRACT FROM AUTHOR]

Let S s * be the class of normalized functions f defined in the open unit disk D = { z : | z | < 1 } such that the quantity z f ′ (z) f (z) lies in an eight-shaped region in the right-half plane and satisfying the condition z f ′ (z) f (z) ≺ 1 + sin z (z ∈ D). In this paper, we aim to investigate the third-order Hankel determinant H 3 (1) and Toeplitz determinant T 3 (2) for this function class S s * associated with sine function and obtain the upper bounds of the determinants H 3 (1) and T 3 (2) . [ABSTRACT FROM AUTHOR]

Let S l * denote the class of analytic functions f in the open unit disk D = { z : | z | < 1 } normalized by f (0) = f ′ (0) − 1 = 0 , which is subordinate to exponential function, z f ′ (z) f (z) ≺ e z (z ∈ D). In this paper, we aim to investigate the third-order Hankel determinant H 3 (1) for this function class S l * associated with exponential function and obtain the upper bound of the determinant H 3 (1) . Meanwhile, we give two examples to illustrate the results obtained. [ABSTRACT FROM AUTHOR]

In this paper, the authors introduce an upper bound of the longitudinal elastic modulus of unidirectional fibrous composites to strength of materials approach, provided that the fibre is much stiffer than the matrix. In the mathematical derivations resulting in this bound, the concept of boundary interphase between filler and matrix was also taken into consideration. The novel element of this work is that the authors have not taken into account any particular variation law to approach the stiffness of this intermediate phase. The theoretical predictions were compared with those obtained from some accurate analytical models as well as with experimental data found in the literature, and a satisfactory accordance was observed. [ABSTRACT FROM AUTHOR]

The process of upsetting, with rotating dies, is used to reduce the force required to deform the workpiece and to receive more homogeneous deformation compared to the same process without the rotational motion of the dies. The upper bound method is an efficient tool for a quick estimate of process parameters. The accuracy of upper bound solutions depends on the chosen class of kinematically admissible velocity fields. The present paper provides an efficient method for choosing kinematically admissible velocity fields that satisfy some stress boundary conditions if the associated flow rule is considered. The method applies to the upsetting of cylinders. It is expected that it leads to accurate solutions if friction is high enough. Besides, the kinematically admissible velocity field accounts for a rigid region near the axis of symmetry. Such a region inevitably occurs in exact solutions because the friction stress must vanish at the axis of symmetry. The final expression for the upper bound, on a combination of the force and torque, involves two arbitrary parameters. These parameters are determined using the upper bound theorem. An example is provided to illustrate the method. [ABSTRACT FROM AUTHOR]

In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the Bayesian and non-Bayesian errors. The consideration of non-Bayesian errors is due to the facts that most classifiers result in non-Bayesian solutions. For both types of errors, we derive the closed-form relations between each bound and error components. When Fano's lower bound in a diagram of "Error Probability vs. Conditional Entropy" is realized based on the approach, its interpretations are enlarged by including non-Bayesian errors and the two situations along with independent properties of the variables. A new upper bound for the Bayesian error is derived with respect to the minimum prior probability, which is generally tighter than Kovalevskij's upper bound. [ABSTRACT FROM AUTHOR]

We consider the independent sum of a given random variable with a Gaussian variable and an infinitely divisible one. We find a novel tight upper bound on the entropy of the sum which still holds when the variable possibly has an infinite second moment. The proven bound has several implications on both information theoretic problems and infinitely divisible noise channels' transmission rates. [ABSTRACT FROM AUTHOR]

We consider series systems built of components which have independent identically distributed (iid) lifetimes with an increasing failure rate (IFR). We determine sharp upper bounds for the expectations of the system lifetimes expressed in terms of the mean, and various scale units based on absolute central moments of component lifetimes. We further establish analogous bounds under a more stringent assumption that the component lifetimes have an increasing density (ID) function. We also indicate the relationship between the IFR property of the components and the generalized cumulative residual entropy of the series system lifetime. [ABSTRACT FROM AUTHOR]

Hydrogen (H2) is an industrial gas that has showcased its importance in several well-known processes such as ammonia, methanol and steel productions, as well as in petrochemical industries. Besides, there is a growing interest in H2 production and purification owing to the global efforts to minimize the emission of greenhouse gases. Nevertheless, H2 which is produced synthetically is expected to contain other impurities and unreacted substituents (e.g., carbon dioxide, CO2; nitrogen, N2 and methane, CH4), such that subsequent purification steps are typically required for practical applications. In this context, membrane-based separation has attracted a vast amount of interest due to its desirable advantages over conventional separation processes, such as the ease of operation, low energy consumption and small plant footprint. Efforts have also been made for the development of high-performance membranes that can overcome the limitations of conventional polymer membranes. In particular, the studies on graphene-based membranes have been actively conducted most recently, showcasing outstanding H2-separation performances. This review focuses on the recent progress and potential challenges in graphene-based membranes for H2 purification. [ABSTRACT FROM AUTHOR]

It is known that the classical ruin function under exponential claim-size distribution depends on two parameters, which are referred to as the mean claim size and the relative security loading. These parameters are assumed to be unknown and random, thus, a loss function that measures the loss sustained by a decision-maker who takes as valid a ruin function which is not correct can be considered. By using squared-error loss function and appropriate distribution function for these parameters, the issue of estimating the ruin function derives in a mixture procedure. Firstly, a bivariate distribution for mixing jointly the two parameters is considered, and second, different univariate distributions for mixing both parameters separately are examined. Consequently, a catalogue of ruin probability functions and severity of ruin, which are more flexible than the original one, are obtained. The methodology is also extended to the Pareto claim size distribution. Several numerical examples illustrate the performance of these functions. [ABSTRACT FROM AUTHOR]