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Buy Till You Die
The Buy Till You Die (BTYD) class of statistical models are designed to capture the behavioral characteristics of non-contractual customers, or when the company is not able to directly observe when a customer stops being a customer of a brand. The goal is typically to model and forecast customer lifetime value. BTYD models all jointly model two processes: (1) a repeat purchase process, that explains how frequently customers make purchases while they are still "alive"; and (2) a dropout process, which models how likely a customer is to churn in any given time period. Common versions of the BTYD model include: * The Pareto/NBD model, which models the dropout process as a Pareto Type II distribution and the purchase frequency process as a negative binomial distribution * The Beta-Geometric/NBD model, which models the dropout process as a geometric distribution with a beta mixing distribution, and models the purchase frequency process as a negative binomial distribution. The co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Customer Lifetime Value
In marketing, customer lifetime value (CLV or often CLTV), lifetime customer value (LCV), or life-time value (LTV) is a prognostication of the net profit contributed to the whole future relationship with a customer. The prediction model can have varying levels of sophistication and accuracy, ranging from a crude heuristic to the use of complex predictive analytics techniques. Customer lifetime value can also be defined as the monetary value of a customer relationship, based on the present value of the projected future cash flows from the customer relationship. Customer lifetime value is an important concept in that it encourages firms to shift their focus from quarterly profits to the long-term health of their customer relationships. Customer lifetime value is an important metric because it represents an upper limit on spending to acquire new customers.Farris, Paul W.; Neil T. Bendle; Phillip E. Pfeifer; David J. Reibstein (2010). ''Marketing Metrics: The Definitive Guide to M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lomax Distribution
The Lomax distribution, conditionally also called the Pareto Type II distribution, is a heavy-tail probability distribution used in business, economics, actuarial science, queueing theory and Internet traffic modeling. It is named after K. S. Lomax. It is essentially a Pareto distribution that has been shifted so that its support begins at zero. Characterization Probability density function The probability density function (pdf) for the Lomax distribution is given by :p(x) = \leftright, \qquad x \geq 0, with shape parameter \alpha > 0 and scale parameter \lambda > 0. The density can be rewritten in such a way that more clearly shows the relation to the Pareto Type I distribution. That is: :p(x) = . Non-central moments The \nuth non-central moment E\left ^\nu\right/math> exists only if the shape parameter \alpha strictly exceeds \nu, when the moment has the value :E\left(X^\nu\right) = \frac Related distributions Relation to the Pareto distribution The L ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negative Binomial Distribution
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of successes (denoted r) occurs. For example, we can define rolling a 6 on a die as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success (r=3). In such a case, the probability distribution of the number of failures that appear will be a negative binomial distribution. An alternative formulation is to model the number of total trials (instead of the number of failures). In fact, for a specified (non-random) number of successes (r), the number of failures (n - r) are random because the total trials (n) are random. For example, we could use the negative binomial distribution to model the number of days n (random) a certain machine works (specified by r) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number ''X'' of Bernoulli trials needed to get one success, supported on the set \; * The probability distribution of the number ''Y'' = ''X'' − 1 of failures before the first success, supported on the set \. Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of the number ''X''); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. The geometric distribution gives the probability that the first occurrence of success requires ''k'' independent trials, each with success probability ''p''. If the probability of succe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta Distribution
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval , 1in terms of two positive parameters, denoted by ''alpha'' (''α'') and ''beta'' (''β''), that appear as exponents of the random variable and control the shape of the distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines. The beta distribution is a suitable model for the random behavior of percentages and proportions. In Bayesian inference, the beta distribution is the conjugate prior probability distribution for the Bernoulli, binomial, negative binomial and geometric distributions. The formulation of the beta distribution discussed here is also known as the beta distribution of the first kind, whereas ''beta distribution of the second kind'' is an alternative name for the beta prime distribution. The generalization to mult ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixture Distribution
In probability and statistics, a mixture distribution is the probability distribution of a random variable that is derived from a collection of other random variables as follows: first, a random variable is selected by chance from the collection according to given probabilities of selection, and then the value of the selected random variable is realized. The underlying random variables may be random real numbers, or they may be random vectors (each having the same dimension), in which case the mixture distribution is a multivariate distribution. In cases where each of the underlying random variables is continuous, the outcome variable will also be continuous and its probability density function is sometimes referred to as a mixture density. The cumulative distribution function (and the probability density function if it exists) can be expressed as a convex combination (i.e. a weighted sum, with non-negative weights that sum to 1) of other distribution functions and density funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Management Science
Management science (or managerial science) is a wide and interdisciplinary study of solving complex problems and making strategic decisions as it pertains to institutions, corporations, governments and other types of organizational entities. It is closely related to management, economics, business, engineering, management consulting, and other fields. It uses various scientific research-based principles, strategies, and analytical methods including mathematical modeling, statistics and numerical algorithms and aims to improve an organization's ability to enact rational and accurate management decisions by arriving at optimal or near optimal solutions to complex decision problems. Management science looks to help businesses achieve goals using a number of scientific methods. The field was initially an outgrowth of applied mathematics, where early challenges were problems relating to the optimization of systems which could be modeled linearly, i.e., determining the optima (Maxima an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
