Product Sales Analysis:Sales Potential vs. Sales Growth

Business Intelligence SolutionsJanuary 2015

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Objectives

• Better understand the relationship between Product Sales Unmet Potential and Product Sales Growth

• Study correlation between Potential and Growth variables using non-parametric correlation analysis

• Evaluate usefulness of new copula apparatus in sales dependence analysis

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Product Sales Unmet Potential vs. Product Sales Growth(360 observations data set)

Product Unit Unmet Potential

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Product Dollars Unmet Potential

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Correlation = - 0.14P-value = 0.006

Correlation = - 0.35P-value < 0.0001

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Relationship between Sales Growth and Sales Unmet Potential variables

• Correlations between Product Sales Growth and Product Sales Unmet Potential variables are highly significant and negative

• On average, the larger the growth of sales, the smaller sales unmet potential

• The highest negative correlation (-0.35 ) is between Product Dollar Growth and Product Dollar Unmet Potential

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Product Unit Unmet Potential Distribution

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Histogram and Best fit distribution Cumulative empirical and best fit distribution

Blue – actual dataRed – fitted Dagum distribution

Mean = 589 unitsMedian = 523 units

Dagum distribution - best fit out of 15 candidates

Product Unit Growth Distribution

Mean = - 836 unitsMedian = - 550 units

Burr distribution - best fit out of 5 candidates

Histogram and Best fit distribution Cumulative empirical and best fit distribution

Blue – actual dataRed – fitted Burr distribution

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Empirical Copula for 2-dimensional Product Potential – Growth Unit data

Product Unit Unmet Potential percentiles

Data (original 360 observations)

Product Unit Unmet Potential percentiles

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Fitted Copula (generated 360 observations)

Note: Product Unit Unmet Potential percentiles are calculated using fitted Dagum distribution, and Product Unit Growth percentiles are calculated using fitted Burr distribution

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Empirical Copula for 2-dimensional Product Potential – Growth Unit data

Product Unit Unmet Potential percentiles

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360 data points

Red dots are actual values, blue dots are predicted values

This copula can be used to estimatefeasibility of product Growth givenUnmet Potential by evaluation Probabilities Pr(Growth >=a | Potential >= b),Pr(Growth >=a , Potential >= b),maxPr(Growth >=a | Potential >= b) {a}for different thresholds a and b

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Bivariate Clayton copula (best fit): generated 1000 data points on percentile scales

Clayton copula is an asymmetriccopula that exhibits greaterdependence in the negative tail

than in the positive

This copula can be usedto estimate feasibility of Growth given UnmetPotential by evaluation Probabilities Pr(Growth >=a | Potential >= b)for different thresholds a and b 9

Bivariate Clayton Copula (best fit) vs. Empirical copula for Product Unit Potential and Growth Unit

360 data points

Empirical Copula

Clayton Copula

1000 data points

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Copula and Feasibility Evaluation of Product Sales Growth Plan

• X is customer level estimated product sales unmet potential in dollars– for selected list of customers total potential Potential = sum(X)

• Y is customer level product sales growth in dollars – according to the plan, product sales growth Growth =

sum(Y) should be greater or equal to g_plan for selected list of customers

• Plan feasibility can be estimated by the following metrics:– Pr(Growth >= a, Potential>=b) as a function of two thresholds a and b– Pr(Growth >= g_plan, Potential>=b) as a function of the only threshold b– max Pr(Growth >= a, Potential>=b) for all a from (a1, a2) as a function of

threshold b– These probabilities can be estimated by copula

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Concept of Feasibility of Product Sales Growth Plan

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Pr(Growth >= a | Potential>=b)

a1 g_plan a2a

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0.5

Pr(Growth >= a | Potential>=b1)

Pr(Growth >= a | Potential>=b2)

Pr(Growth >= a | Potential>=b3)

max { Pr(Growth >= a | Potential>=b)} for all a, b

Note: promotion efforts are involved in potential estimation, therefore, promotion is taking into account indirectly in evaluation of probability Pr(Growth >= a | Potential>=b). On the other hand, copula allows to take promotion into account directly and estimate probability Pr(Growth >= a | Potential>=b, Promotion >=c).

Summary• Product Sales Unmet Potential is not Product Sales. Product Sales Unmet

Potential is an additional maximum value that can be generated by product sales during next year in principle if the promotion efforts and the mechanism of data generation will be the same

• All three non-parametric measures of association (Spearman, Kendall, and Hoeffding) are indicative of existing strong correlation between Product Unmet Potential and Product Growth variables

• Product Unit Unmet Potential is negatively correlated with Product Sales Growth:– - 0.35 for Unit Growth– - 0.14 for Dollars Growth

with p-value < 0.001 (Spearman correlation) • Copula is useful approach to estimate dependence structure in multidimensional settings, especially tail

dependence, and evaluate probability of any event, and in particular, feasibility of a planned product growth

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